Well, yeah, we made it back. You know where I'm at by now. You recognize this place. Been training here a lot in this block. And yes, the work does not stop, ladies and gentlemen. Even though we are tapering, the work does not stop. Remember, I want to arrive at the starting line as fit as possible and as fresh as possible. So obviously, when you're talking about tapering, you're talking about decreasing your volume so your legs can freshen. But I still have time to work with. What is it now when you're watching this about 11 days to fine-tune, refine, sharpen the legs, sharpen the mind? The aerobic base is basically set. Like, you're not going to really advance there too much. But I'm not afraid to put in some more work before Pike's peak, so that's what I'm doing today. And yes, keyword is work. And question of the day, I like this one a lot. How, oh, baby. How has long distance running taught you or infused into you as a person the ethic of work or work ethic? Like, how have you? So what I'm getting at is when I say seek beauty, work hard, and love each other, that's what we're focused on today. Because I want to share with all of you where my angle and where I'm coming from, when I say that every single day at the end of the vlog, I'm not just saying that for, I don't know, a catchy motto or a catchy way to end the vlog. I really, really mean it, all right? So today we're working. We're working on the uphill. We're getting close. This is not the last uphill, but we're getting closer. So thank you for being here. I can't wait to read your thoughts on work ethic down below in the comments. Connecting it to long. OK, one last point before we dive in. And I'm going to start getting ready with a B roll here. Basically, for all the high schoolers out there, you have no idea the gift that you are being given right now as a cross country or long distance runner in track.  I had no idea when I was in high school, even a little bit in college, what kind of wisdom and, again, work ethic I was being given as a long distance runner, because it's sacrifice. It's the pain cave. It's doing things you don't want to do. Like nobody really wants to go out and run 20 miles on Sunday morning when everyone else is sleeping in. It's in college. So all I'm saying is keep going, especially for all the young folks out there. You're setting yourself up for long term success. I promise. I promise. Your work ethic is going to be through the roof. And don't hesitate when you're in a future job interview after college or maybe after high school to tell them that you are a long distance runner and that this has taught you so much about what it means to sacrifice and to work hard. All right, let's get rolling. Work, work. Less talk, more action. Get the job done. Whether it's with your cross training, if you're injured, getting good food in you, taking care of your teammates. You know, if you're still on a team, it's a less talk, more action. Remember last week I told you what I was telling myself on a 14 to run last week? Well, today it's less talk, more action. Get the job done. Working hard, working hard. We're not done working yet in this training block and not done working in the Soccany Mad River TRs. That was the shoe I, a couple of people have been asking, what is this Soccany shoe that Seth is wearing out on the trails? It's called the Soccany Mad River TR. Yes, it is available down below from Running Warehouse. I love it. I love it, I love it. Now I'm only at 33 miles in the shoe, so it's not quite time for a full review, but it's just, it's such a comfortable ride. And today I was going back and forth between Solomon or Soccany and I decided to go Soccany because I was wearing the weighted vest, the 20 pound weighted vest today. And I wanted to just have a little more protection for my knees, my ankles, and just absorb a little more of that, especially the downhill pounding with the weighted vest on. And yes, today's run was 14 miles, 22 kilometers, 5,000 feet of vertical gain and loss or 1,500 meters of vertical gain and loss. And how did it feel? Felt solid, felt okay. So the last time I wore the vest, I went, I went eight miles. So today was 14, so not quite double. And just so you know, that was the last time I'll wear the vest in this training block. Don't worry, but I'm feeling pretty darn strong. In fact, those four, so I did four strides and then some forum drills afterward. That's what I was doing by my car there after the run. And as soon as I took the vest off and I did those four strides, like I was loud.  So anyway, solid day up on Grace Peak today. And let's dive into work ethic. Oh man, I love it. I love working hard. I love, just so you know, true love and I, we just got back from date night. So I love leisure. I love rest. I love like good drinks and sitting around pools and sitting on beaches and just chilling. Like I love that, but I also love working hard. Like I think it's a good to have a balance. And just so you know, huge rainstorm is rolling in right now. So if you hear the thunder, I'm just looking out to make sure everything's all right out in my backyard. So it was an amazing day. Now, where did I learn my work ethic? Definitely from my dad. He was a former runner. Now he's just a big time hiker and walker. He doesn't run anymore. He's in his early sixties now. And he ran Pikes Peak probably at least eight times like the Pikes Peak ascent big. He was pretty accomplished runner back in the day. He won a couple local trail, but this is like back in the seventies and the eighties when trail running was not really at the top of everyone's to-do list. If you know what I mean, compared to today where there's a big strong community of trail running. So he worked very hard at his career. So what did he do? He sold life insurance. He helped people with investments, but he did it the right way. You know what I mean? He worked for I think 32 years and then retired and now he's enjoying the grandchildren. But I'm telling you like, I don't, I can only think of maybe one or two other people that I don't even know personally but people that I've heard of who might approach my dad's work ethic. Even to this day in his retirement, taking care of all the grandkids but like going on adventures with him. Like he just loves to do things. And anyway, so he passed that work ethic on to me. And frankly, as a seventh grader, as I was transitioning away from soccer, which I bet is the story for many runners out there. I was transitioning away from soccer because I could not kick a soccer ball. First of all, soaking wet, I weighed about 95 pounds. And so my legs were teeny tiny chicken legs and I could not kick a soccer ball from the corner kick to the goal. And like at that point in seventh grade, sorry, just thought I heard thunder, we're good. At that point in seventh grade, I said, okay, I'm eliminating the soccer ball and we're just going to run. So anyway, that's how I got started into running and my dad really invited me to start waking up at 5.30, 6 a.m. and go run with him before he went off to work. And that's what I did as a seventh grader and frankly haven't really stopped since. Now I've said it once and I'll say it again right now, there's really no luck in long distance running in my humble opinion. It comes down to these three variables for me. Yes, it helps to have a little bit of talent, a little bit of talent helps. A sound training plan, training philosophy really helps as well. And then number three, work ethic. Listen, we're not shooting pucks at a net and it hits the crossbar and bounces in. We're not doing an onside kick and football and the ball happens to bounce the right way or you hit a baseball and depending on how the dirt is groomed that day will determine on whether the ball rolls foul or rolls fair.  And I don't know if you don't have to call it luck. You can call it whatever you want but I just believe running comes down to your fitness and how well you trained and how hard you worked. But balancing that, remember, walk the line between fitness and freshness. So I'm a big proponent of working hard. That's why I say it every day and not just in running but in our careers, in our family life, in our relationships, in taking care of the house and being frankly, and this is, I'd like to work better, be better at this as well but being a strong contributor to our communities that we live in, I don't know. I just gotta find more time to figure out how to do that but so anyway, that's what I'm talking about when I say work hard at the end of every vlog. Like I wanna live by it and I want you guys to hold me accountable to live by that and I'll do my best through DeMord Global running on Strava to help you live by that as well if you want to. And I think is for success in long distance running, it really does come down to that consistency and that work ethic. And so with that said, yes, that is the last vest run. I didn't necessarily wanna put that vest on today but I wanted to work hard today so I said, okay, let's do it one more time in this training bar. Let's do this, all right? Let's do it and that's what I did and I got it done and it's all about that up here between the ears to make that happen. So I love you guys and if you wanna dive a little more into mental toughness, click on that box on the left and if you wanna click on the box on the right, that'll take you to a vlog where I really went to the well in a hard, hard long run. All right, I love you guys. Thanks for being here. Thanks for watching. See beauty, work hard and love each other. See you tomorrow.


God created man to be a resting place. So with Adam he walked in the cool of the day. Noah built an ark because God strove with man till Abraham was picked, the father had a plan. Why pick a people? Why choose a nation? Simple, the Savior needs a lineage, a family, a location. So God freed his nation from Pharaoh's oppression. Not to build their own Egypt, he delivered them for worship. God asked for a tent somewhere he could rest. Moses built the altar with a radiant face. But God didn't want sacrifice for the sake of appeasement. He longed for intimacy, for closeness, for agreement. So when David got the ark, he didn't lock it away. He erected a new tent and worshiped night and day. Finally a place where God's presence could rest and God's glory stayed while praise was expressed. But sin was a problem, his presence disregarded as the praise tent fell down, God's glory departed. So Jesus brought the seeds of the gardens to the earth. That's why the angels cried glory the night of his birth. The cross tore the veil, separation dispelled. His spirit now could live inside of us to dwell. A nation of priests, the kingdom of hosts, the temple of God went global and remote. If worship's unceasing right now around the throne, Jesus prayed here on earth like in heaven, as it's shown. Gather even more as the day's drawing close. Rebuild David's tent from the islands to the coast. Every home and altar, every church, a house of prayer, a welcome party for Jesus when we meet him in the air. A thousand year reign to get the earth ready for the garden city, the new Jerusalem will descend down from heaven. No tears, pain or darkness, the last will see night. For his glory will dwell, the lamb is its light. Behold the tabernacle of God is with man, at last a resting place, a garden forever. Amen. Amen. Not gonna lie, the 11 a.m. gave me a really terrible golf clap and I almost didn't do the poem for the second service because of that. But I love the 11. I'm Pastor Caleb, I'm here. And one of the worship pastors here wanna say hello to those in Portage and online. And this poem is what we're gonna be talking about this morning. We're talking about the resting place for God. The sermon title is Every Home and Altar and we're continuing on our ax series. So go ahead and turn to Acts 15. But we're starting, before we even read the scripture, we're starting with the question that I hope you've been asking and that we should be asking, which is what is God doing on the earth today? We're so focused on what is happening in the kingdom of darkness, but we serve a God who is always initiating. God is not a reactive God. He's not, the enemy doesn't do something. He's like, oh my gosh, I gotta figure out a plan. He's the one who's in control. He's always moving. And today we're gonna look at one of the great prophetic promises for this time right now, the scripture that's talking about this day and age to see what God is doing on the earth. And so I hope you are ready to receive that. I hope you've been asking the question. We're gonna kinda look at this scripture together. We're gonna read a lot of Bible. Is that okay with you guys this morning? Hope so.  You're not gonna think about the Richland meat market brats that you're gonna eat after the 11 a.m. service. You're gonna focus. Acts 15, starting in verse one. And certain men came down from Judea and taught the brethren, unless you are circumcised according to the custom of Moses, you cannot be saved. Therefore, when Paul and Barnabas had no small dissension and dispute with them, they determined that Paul and Barnabas and certain others of them should go up to Jerusalem to the apostles and the elders about this question. So being sent on their way by the church, they passed through Phoenicia and Samaria, describing the conversions of the Gentiles and they caused great joy to come to the brethren. When they came to Jerusalem, they were received by the church and the apostles and the elders, and they reported to the things that God had done with them. But some of the sect of the Pharisees who believed rose up saying, it's necessary to circumcise them and to command them to keep the law of Moses. Now the apostles and elders came together to consider the matter. And when there had been much dispute, Peter rose up and said to them, men and brethren, you know that a good while ago, God chose among us that by my mouth, the Gentiles should hear the word of the gospel and believe. So God who knows the heart, acknowledged them by giving them the Holy Spirit, just as he did to us. And he made no distinction between them, purifying their hearts by faith. Now therefore, why do you test God by putting a yoke on the neck of the disciples, which neither our fathers nor we were able to bear? But we believe that through the grace of the Lord Jesus Christ, we shall be saved in the same manner as they. Then all the multitude kept silent and listened to Barnabas and Paul, declaring how many miracles and wonders God had worked among the Gentiles. And after that, after they had become silent, James answered saying, men, brethren, listen to me. Simon has declared how God has first visited the Gentiles to take out of them a people for his name. And with this, the words of the prophets agree just as it's written, after this, I will return and I will rebuild the tabernacle of David, which has fallen down. I will rebuild its ruins and I will set it up so the rest of mankind may seek the Lord. Even all the Gentiles who are called by my name says the Lord who does all of these things, amen. I love this scripture because it's the messy church in the middle of revival. We sometimes romanticize revival in this idea of everybody's just in perfect harmony. There's no issues and problems, but of course, the book of Acts is showing the church in Jerusalem that has a major problem in the sense of they are half Pharisees or people that have followed the traditions of the Mosaic law to the T. And now you have revival hitting among the Romans and the Greeks and those from all over the place.  And this empire, it was a wicked time. I mean, these people could have been just months ago been involved in orgies and sacrificing the idols and all types of unbelievably horrific things. And all of a sudden they're all slammed in one church together and you have a mess where you just have different people and social, economical differences, racism, all of these things. And so you see this doctrine kind of pops up in the midst of this revival that says, hey, you have to be circumcised to be saved. And it really tickles the ears of the Pharisees because they are all circumcised. Notice everybody who's already had the circumcision is on board. They've already received the circumcision and they've also been following the laws. And so it's like, hey, we've had to sacrifice so much. These guys should have to sacrifice too, which is a tough evangelistic cell. It's hard to be like, hey, God loves you and has a wonderful plan for your life. You're saved by grace through faith, but there's this one thing you gotta do.  Like, it's a tough sell. But you understand that to them, it was a major marking of who they were.  And so I love the heart of the apostles though.  They use stories. Listen, this is Bob, Bob the electrician. And his whole family got saved. His 10 year old girl couldn't walk and now she's walking. And now he's saving everybody at his shop. And then they start telling the stories of God moving among the Gentiles. So they're sharing these testimonies. And then I love the heart of James. As everybody's sharing testimony, James stands up and he's my guy because he's like, let's take a second to get some prophetic understanding of what's happening. He's asking that question, God, what are you doing in the earth today? Cause we're talking really about kind of a specific rule, but James, he says, listen, what is God doing as a whole? And he brings this beautiful passage from Amos 9-11 where God says, I will rebuild the tabernacle of David. I will restore its ruins. And in this, he says, the Gentiles are going to seek the Lord. And what James is saying here is, listen, this isn't about circumcision or uncircumcision. This is about God receiving the worship that's due his name. And this is what God's doing. He's bringing in the Gentiles at this time. It's a powerful statement that James is making. And I think it's missed a lot of times because we are so used to temple language. And of course the temple's in the New Testament. Jesus says, I'm the temple. And then we know that from 1 Corinthians that our bodies are personally the temple of the Holy Spirit because Jesus tore the veil. But here we have not the temple, but the stage before the temple called David's Tabernacle highlighted with this prophetic promise from Yahweh saying, I'm going to, before Jesus comes back, I'm going to do this brand new thing. And so to understand it, we have to understand God's desire for a resting place and for a dwelling place. And so when we say temple and we say tent, what's the difference here? And so I just have four words. I hope this kind of sticks with us, but individual temple, that's you, corporate tent. You yourself individually temple of the Holy Spirit. Corporately we are a tent. We are the tabernacle of God. And so to obviously understand what is David's Tabernacle? Why is it important? What does it mean that God's going to rebuild it? We have to go back kind of to the origins of the temple and tabernacle. And so that we go all the way back to Exodus when God frees his people for worship. We see in Exodus 19, five through six, God pauses, he's such a good father. He just, he fathers Israel so well. He brings them out, he saves them from Egypt. And then what is, what's the first thing?  The father and mother name them, right? They give them definition and identity through a name. Well, that's exactly what the father does. He brings them across the Dead Sea and then he names them and gives them identity in Exodus 19, five. Now therefore, if you will indeed obey my voice and keep my covenant, then you shall be a special treasure to me above all people, for all the earth is mine and you shall be to me a kingdom of priests, a holy nation, these are the words which you shall speak to the children of Israel. Now this is a big point, pay attention. This is a big point that a lot of people miss because they think the priesthood, New Testament reality, we're all priests, Old Testament, there's only a couple priests.  Well, what is a priest?  Well, let's look at what Exodus 28 and 29 say. Go ahead and put that slide up there. God, when he defines the priesthood six times and six is the number of man, God uses it to define things like everything was made in six days, six times God says this phrase that he or they may minister to me as priests. What is the primary calling of a priest? It's to minister to God. What does that mean minister to God? You might be like, I'm not in ministry, I don't know what that means. It just means to give him glory and honor and he takes delight in that. He really loves you a ton. You make a lot of mistakes and you're really messed up. That's the bad news, but God, he still sees and he loves and he delights in you.  It is what he is wanting and what he's looking for. A people that minister to him. But what did, how did Israel receive this revelation of a God who wants everyone to draw near? Well, they saw him moving on the mountain and they built a golden calf and they said we'd rather have one of these kind of Egyptian style gods and we want to keep God at a distance. We love the protection and atonement part. That stuff's awesome.  We love that, but your presence and your personhood, that scares me. I don't want that. I want somebody to do that for me. And so for 400 years, Israel had a tent in the middle of their camp and in this, the Ark of the Covenant, it's where God's presence rest has cabowed the weight of who he is between the cherub and it rest and dwelt to be visited once a year by the high priest on the day of atonement. God was amongst the people, but he was isolated from the people and for 400 years, we don't see anybody complain or question that. Everyone seems to be cool with it. Then one day pressure comes and the Philistines are rising up against Israel. Eli's the prophet slash judge and his sons are evil. They've been sleeping with temple prostitutes. They've been desecrating me. And so all of a sudden this rises up and they've perverted the priesthood and they say, oh, I know what to do. We grab the Ark of the Covenant, we just trotted out there and God will just magically defeat the enemies. We'll put it back and go back to our lifestyle. God won't be handled, restrained or controlled, but he will be hosted by people who want him. They didn't want him.  That's what the enemy's doing. Well, what was God doing in the earth? God at the same time that Ark was being captured, he got this little boy in the back hills of Bethlehem and he didn't have proximity to the Ark of the Covenant but he had his own holy of holies called the back hills of Bethlehem where he worshiped and he prayed and the delight and glory of God dwelt and rested on him and Samuel anointed him and David went on a 26 year journey to become king. And at the end of the journey he unites the kingdoms becomes king. It's time to bring the Ark of the Covenant back to Israel. It's time to restore the presence back to Moses' tent. He goes and gets the Ark and he has a kingly robe on and the person who's carrying it in a cart, Uzzah, got comfortable with the presence, reached out and touched the Ark. But God will not be handled, restrained or controlled. He will be hosted by people who want him. He tried to handle God and Uzzah died. David went away angry, offended. What the heck? I just came to be king to bring your presence back and this is how you treat me. He's angry. He goes back to Jerusalem. And this guy named Obed Edom arises and changes history forever. Obed Edom was half Levite, half Philistine and this guy after seeing the death and the turmoil that's been happening for 26 years on the Ark of the Covenant, he does something that few would ever dare to do. He said, yeah, you know that object that's been killing people nonstop? Yeah, go ahead and put that in my living room. I'm about you, if there was a thing where it's like all Samsung TVs are exploding and killing everybody when you turn them on, like I wouldn't be like, man, let's get a Samsung and just put it in our living room and just, this is great, you know? Like I'm thinking if I have to take the Ark then I'm putting it all the way on the corner of my lot and building a little shed and then a wall and then another wall and we're never gonna look and never gonna think, never gonna do anything. We're just gonna pretend it's not over there and one day hopefully it disappears. But Obed Edom understood something about the God who chose a nation of priests and he brought the presence of God to the center of the home. He didn't have a sacrificial system. He wasn't slaughtering bowls and goats. He wasn't offering incense. He didn't have a table to show bread. He just had the presence and God just simply arrested. And David's kind of waiting. He's like, you know, he's waiting for the news story to break. Like News Flash, Obed Edom and his family, they all die, Raiders of the Lost Ark style where they all just like are viscerated by like lasers coming out of the Ark. He's waiting for the story, but then what comes back is, have you heard the news? Obed Edom got promoted at his job. His wife won a beauty contest. The kids are all like making varsity basketball and God is blessing everything and David gets provoked. And David goes to get the Ark again. And remember last time he wore the kingly garment? David was from Judah. That's the lineage where the Israel kings were from. Well, this time he took off the kingly garment. You know what he put on? An ephod. Who wore the ephod? The priests. The priests were the Levites. If you're from Judah, you couldn't be a priest. Well, here we go. David understood the heart of a father that said he wanted a kingdom of priests and a priest is somebody who ministers before the Lord. He takes off the kingly robe. He puts on the ephod.  And that's the part of the story that most people latch onto. And it's obviously insanely powerful. It's been used by people who like, have disrupted church services for thousands of years. Like David danced in his underwear. I can take my shirt off. Like, no, no, that's not what happened. David in this moment is taking the ark and it's going back to the Tabernacle of Moses. This is so exciting. They get to Gibeon where it's time to take a left turn and bring the ark back. And David shocks everybody. When he's supposed to take a left, he takes a right. And he makes a beeline for the city of David and goes right to the top of Mount Zion. And he's built not a Tabernacle with three compartments in it, but a tent with one big open space. And he brings the presence of God in at the center. And then he gets 4,000 Levite singers and 288 Levite musicians. And they begin to play and worship. I like to think like, because this was such a revolutionary moment. I was like, well, who would have been like, to have been like the first worship leader in that Tabernacle? You know, like you're like, David, are you sure we can do this? Like, I didn't read any scriptures about this. Are you sure? Because it's kind of the ark. Like you're just kind of like going to lead worship and you talk about pressure worship. Like sometimes you're like, man, what happens if I don't open with the right song? Like congregation might be mad at me. She's like, man, what if I open with the wrong song God kills me. He just, in that moment, the presence and power of God. And instead of killing everybody, instead of God being angry, instead of God rejecting the opposite happens where God dwells amongst man and his presence fills the tent and his glory fills the tent and revival spills out into Israel. Israel went from silence to song in a year. There was no corporate worship services. There were no songs that were written for the, and now you have an explosion of worship songs and prayer songs. People are having prophetic visions of Jesus and the end times and homes have gone from silence to being filled with singing and music and prayer and the landscape has completely shifted. God now is breaking out of the compartment and he's filling his people. We sang it earlier, Psalm 22, he inhabits. God lives in, he dwells, he rests. He puts his feet up, so to speak, in the praises of his people. And this tabernacle of David changed everything in history forever. Now we remember that James said, in the last days, I, meaning God, I'm gonna rebuild the tabernacle of David. You didn't say I'm gonna rebuild that temple because what, the temple's the individual, right? Unless you there, there's no engaging with it. But a tabernacle, a tent is global. We can't build a billion dollar temple, right? But we can buy a $50 tent from Walmart, right? We can go camping anywhere, that's the point of camping. That's why we all do it. What we love in Michigan too, I mean, it's like, everyone's like, let's live like homeless people all summer and everyone loves it. It's like, it's amazing. I'm not a big camper, as you probably can't tell, but I have a biblical courtship with nature. We will spend the day together. But then at the evening, we say good night. I go into my bed, nature has her bed, and it's, it works out great. But when you're, what's the thing with a tent? It's now, it's global, it's everywhere, and it spills out that people could hear the worship and praise happening all over Jerusalem. The trade routes that went right by Jerusalem, they're walking by for years, it's been silent, and all of a sudden, they hear shouting and screaming and dancing, they're like, what in the heck is going on in Jerusalem with this tent? It's exploding all over the earth. And God said he's gonna rebuild that. So let's ask the question, why a tent? Why a tent? The first is the spiritual legacy. David changed history because he built the tabernacle of David. Did you know that the seven times that Israel came back to God, the seven revivals of Israel, every single time they re-instituted the Davidic form of worship? So that worship expression, didn't just live on in David's day, but it was Solomon and Jehoshaphat and Hezekiah and Ezra and Nehemiah. All of these leaders, every time they move back to God, you know what they do? They take worship and prayer and they put it back at the center. The legacy from that, I wanna look at Obed Edom, because Obed Edom's kind of the man. Here's a guy who couldn't be in the priesthood because he's half Philistine, which the Israelites looked down on worse than if he was just a full Philistine.   And here's a guy who seemingly is not qualified to host the presence of God. And then he brings it in and hosts his presence, but what's beautiful is this is not where Obed Edom's story ends. It says later that he became a gatekeeper, a doorkeeper in the house of his God. Before Obed Edom was probably living for himself, his house, his family, it was just about what he could pass on to his kids financially, their education, their success. And the narcissism of his world got interrupted by three months in the presence of God. And he got consumed with something that was bigger than himself. Well, how did that impact his family? Well, let's see. In first Chronicles 26, one through four. As for the divisions of the gatekeepers, this is naming the gatekeepers. And then it goes says Obed Edom's and then his eight sons for they were men of great ability. This is so incredible to me. One guy chooses three months of saying yes to the presence of God. Every one of his sons, not only are not lost, they're like, we can't wait to be in the house. We just wanna serve the house of God, all eight of them serving the Lord, loving the Lord, worshipers of the Lord, generational blessing on the house of Obed Edom because his yes to say yes to the presence of God. I think of Asaph, this one makes me particularly excited. Asaph was one of the three worship leaders that were the chief worship leaders in David's tabernacle. He wrote 12 Psalms. He was the one David would give Psalms to. You look in the header and sometimes, David would write the Psalm and then he would give it to Asaph to have them lead in the house. And he lived in the most comfortable war free time in Israel's history because of that time. And yet we see the impact of his own worship leading generations later, I wanna read a quick story to kinda show us that in 2nd Chronicles 20, 15 through 22. There's this mystery prophet who rises up. It's a time where Israel's under siege. They might all die, they might be in exile and everyone doesn't know what to do. Should we fortify our defenses? Should we have everybody fight? What's our military strategy? And this mystery prophet arises. And he said, listen, all of you Judah and you inhabitants of Jerusalem and you King Jehoshaphat thus says the Lord today, do not be afraid nor dismayed because of this great multitude for the battle is not yours but God's. Tomorrow go down against them. They will surely come up by the accent, the ascent, excuse me, ascent of Ziz and you will find them at the end of the brook before the wilderness of Jerul. You will not need to fight this battle. Position yourself, stand still and see the salvation of the Lord who is with you. O Judah and Jerusalem, do not fear or be dismayed. Tomorrow go out against them for the Lord is with you. And Jehoshaphat bowed his head with his face to the ground and all Judah and the inhabitants of Jerusalem bowed before the Lord, worshiping the Lord. Now let's look in verse 22. Now when they began to sing and praise, this is the worshipers who've gone before. The Lord set ambushes against the people of Ammon, Moab and Mount Seer who had come against Judah and they were defeated. They put the worshipers in front of the army and they worshiped.  Remember you're supposed to get the Ark of the Covenant and float it out there like a trinket. But God will not be handled, restrained or controlled but he will be hosted by people who want him. They hosted his presence. They worshiped and gave him glory and honor and the Lord did the fighting. Well, who was this mystery prophet? Who would have such an insanely radical idea to worship? Well, let's look two verses before. I'm glad you asked, great question. Second Chronicles, 2014.  Ho, ho, ho, ho. Asaph. Just a worship leader, right? Showing up, singing in the house of God, learning to lead worship. His kids every day, they hear their daddy sing in worship songs and he's in the scriptures. What are you doing, daddy? I'm writing a song to sing in the house of God. And he thinks his worship is just impacting that moment. But somewhere along the line, his son gets into his DNA. Home isn't about me. It's about hosting God's presence. And my daddy knows that when there's trial and tribulation, we rise up and we worship. That's what we do in this family. And that got passed down to his son and that got passed down to his son. And that got passed down to his son. And that son lived in a time that Asaph didn't even live in. Asaph didn't even live in a time where there was these massive wars. But his great, great grandson, under a time of pressure, he had DNA in his system, a legacy of worship and prayer at the center of the home. And he says, King Joseph, fear not. If we worship, then God will do the fighting for us. And the king's heart that was cowardly and scared got bold and got courage and filled with hope. And they took this miraculous, ridiculous idea and they put it on the forefront and God delivered Israel because of one man's worship hundreds of years earlier. Listen, I love these things that I'm gonna say. So I'm not trying to trash these things individually. I have these myself, but your 401ks, your Roth funds, the education that you buy for your kids will help them and will help the next generation. But the legacy of worship and prayer in your home will live on for generations. If your kids see you praying when you start getting stressed out about finances or when there's a family difficulty, they know what we do. We get together as a family and we worship and we pray. And even though we don't feel it, we get up on Sunday mornings and we go into the house of God and we worship together whether we feel like it or not.  This idea of a God who will not be handled, restrained or controlled, but he will be hosted by simply people who want him. So why a tent first, it's generational. Next is it's global. Everyone can participate. The tent of God is global.  That's what the whole point of this passage is.  It's global. Why a tent? It's evangel, you can put these on the screen too, go on. Why a tent? It's evangelistic. It becomes a place where God's spirit can rest and Pastor Lee had this picture I wanna show on the screen, this prophetic picture of these tent posts and he saw a picture of a thousand praying churches across America and as individual churches begin to meet as a house of prayer, suddenly we're rebuilding this tabernacle that has fallen, worship and prayer and raising a tent to cover our entire nation under the presence of God. And you know what I see? That breaks down a little bit closer, right? Kalamazoo. I know this is a picture of America, you can leave that slide up there though. If we have a thousand praying churches in America, what if we had a thousand praying families? And each family is like, each individual is like a little tent peg being buried into the ground of the soil of what God is doing in his house and as they're planted into the soil, there's a tent raised for God's presence to be hosted and what if there was a thousand homes in Kalamazoo where places where God's presence could rest that the lost knew if we just go to Suzie's house or Billy's house, we know those people will pray for us. We know they'll be healing and deliverance. We know they'll be the power of God because God rests in this place. This is what God is doing in the earth. Every home and altar, every church, a house of prayer. And what I feel this morning, we're gonna take some time and do some ministry. I felt so strong in the 9 a.m. and I feel even stronger now. There is a attack and assignment of the enemy of shame. And it's interesting because some of you might have seen two weeks ago, one of the things the protestors downtown spray painted across the city center when they were angry after the overturning of Roe v. Wade was the word shame. And I felt like that was this picture of what the demonic is trying to spray paint over the house of God, the word shame. You're not good enough. You're not good enough. Oh, that's great for you, Pastor Caleb.  You don't know how broken my family is. You don't know the generational curses. You don't know A, B, C, D. That's the enemy spray painting shame over your heart this morning in red paint trying to stop what God has assigned you to do. Listen, you know who this all started through? King David. King David was a terrible father, probably a worse husband. He killed somebody. He committed adultery.  I'm like, wow, okay, maybe you did beat David. That's amazing. David is this man who got so many things wrong but he got one thing right and he changed history. He said, I'm not perfect. I don't have, it's not that I haven't made any mistakes. My home isn't clean. I'm a giant mess, but God, I just want you. I just want your presence.  I want to invite you to stand here in Richland and at Portage. And I felt this morning specifically that the Lord is stirring hearts and that even as I was preaching, you felt shame telling you why your house couldn't be part of this movement, why you're not gonna rebuild the tabernacle of David because A, B, C, and D, there is a demonic attack of shame that is coming against the people of God that I believe the Lord wants to lift. And so I actually invited the worship team to come back up and we're gonna take a few moments.  If there are any areas of shame in your heart to just release that to the Lord. And what I felt the Lord wanted to do this morning here in Portage and online was he just wanted us to walk out of those doors knowing that we are a priest that blesses his heart. When he looks at us, he doesn't feel disappointment and anger and sadness like we think he does.   My heart is so moved into light and I know what, you know what, once a week you wrestle your family together in the living room and half of them are fighting and paying attention and you sing one song and it feels horrible but you did it and God's like, I loved it. Oh, I love that time. You're like, what? It was a mess. And God's like, I know I'm in the mess. I just wanna be invited into the mess, into the real life. I want to be invited in, don't let shame steal this rebuilding of what God is doing. So Lord, even as we wait on you for a moment and as the worship team sings, Lord, I ask that you would raise up your house of prayer, Lord, your Levites, Lord, right now that you would strengthen the heart. I ask specifically for mothers and fathers that feel afraid and shameful to pray and worship in front of their kids because of the past. God, I ask for your blood to come and wash over the guilt and the shame and the name of Jesus. Past is covered by the blood.  Hear this cry from the Lord. Let's respond and say, I'll make my home an altar. I wanna pray over married couples who feel difficulty.  And you have shame of the area that you want to pray together but you feel this wall that's like you can't break through it. Lord, I just ask right now that you would break down every attack of the enemy to thwart prayer and marriage, God. Husbands and wives praying together, standing together. Lord, we ask what God has joined together. Let no spirit of shame separate. Lord, let no condemnation separate. Let no heaviness separate, Lord. Whatever walls are standing in the way, Lord. I ask that you would knock them down. Oh God, I ask for a bedrock of praying marriages, Lord. That radiant church, Lord. I ask for husbands and wives and families that pray and worship together in the name of Jesus. Just pray for unity. Lord, we ask whether we're in family or not, Lord. Whether we're single, we live on our own. We live with roommates, we're kids. We're married, we're divorced. Lord, wherever we are at, Lord, we consecrate ourselves. Say, God, we want our homes to be part of this thousand praying families reality in Kalamazoo. God, would you make our home a house of prayer? Would you make our home an altar where your presence can dwell and rest? Would you make our prayer and our worship, Lord? Ascend before heaven, God. We just, we're like David and we just want you. That's all we know, but God, we know. You won't be handled, restrained or controlled, but you will be hosted by people who want you. Jesus, we say right now from this house, we want you. Jesus, we want you. God, we want you. You've been rejected so many times and we've failed so many times but we say from this house, God, we want you. Let's sing this together. That port is online too. Let's sing out again from this house. Prayer partners, I want to invite you guys to come forward. We had a few powerful prayer moments this morning, particularly on that area of shame where the Lord was just doing something, lifting that weight. And if you have any prayer need, we would love to pray with you. If you feel that, like even while I was preaching, you were like, there was something in you that was like, you don't deserve this. You can't do this. You're not good enough for this. Whatever that is, that's the lie of shame and it's from the pit of hell. It is not from the Father and the heart of the Father. And so if that's you and you still feel that, come forward and for everyone else, I hope when you walk out those doors, you feel the delight of the Father. You are walking out with an ephod. You wear the priestly garments. The Lord is delighted in your sacrifice. He is with you. He was for you. And I really believe this. We are going to see God do what he promised. And that passage of scripture 2000 years ago, I believe is gonna be fulfilled in our day.


I do love this 180SX, go between that. Lemondry the Poles. What? We got it? Oh, come on. That was, you can't tell me that that was not sick. What's up, everybody? How are you? We're having, we're here on Forza Horizon 4 in the streets of Edinburgh, and we are in my 240SX.  I was having fun, well, real head motion, drift camera. I was having a lot of fun with the last time this dude was going to come clean by us. Having a lot of fun last time on the mountain. So I wanted to do some street drifting with it. So we're going to rock my 180SX and have a little fun in the streets and see what we can do and how well we can drift to the streets with this. Definitely going to be a fun experience. And this is one of my favorite lower powered drift cars. So we're just going to get right to it. Get that wheel cam turned on and then we're going to go full send. It's like there's somebody there. We're just going to go full send on this. See how this works. Already starting to over rotate a little bit, but. Give me a second to get used to the car and I think we'll be good. Oh, don't hit him. Here we go. Just a little freestyle in the city today in a little 180SX.  Don't hit the mini. As I said, don't hit the mini. It's like he's trying to taint him with us. So that was a nice transition. I don't know if we'll do this in fourth. All this car barely has the power. Oh, look at that sun felt there. So kind of we're able to somewhat get sideways till we lost a little bit of power. Definitely a lot of fun doing street drifting with this camera as we're taking on pylons with this camera for sure. Definitely gives a different dynamic for drifting here in Horizon 4. A lot of breaking there. Well, between these cars, there we go. I am surprised we held that till right there. Almost perfect.  Basically hard parked that thing. Oh, no power going uphill. Oh, we can go through that? I got scared. Pulling China shops would be to get an achievement. So if you guys are enjoying this, let me know. I know some people are wondering how to turn it on. So real quick, it is just under settings, under HUD and all the way down at the bottom right there. You have cockpit drift cam. Make sure you turn it on and adjust your things. I adjusted this up a little bit as well as that to suit my driving style. But that is what we're looking at for today. Oh, that's a Ferrari. Kind of want to do a 4-5-8 build. Come down this street, lay off the clutch. Cut there, run the curve. Oh, that was nice. This makes street drifting so much more enjoyable with this view. It makes me want to stay in this view much more just because it gives it that whole immersion. Oh, we're not going to make that. Oh, we made it. We got a 4-5-8 following us. So he's getting all sideways in our mirror. Hey, buddy. Oh, I should pay attention where I'm going out the mirror. Kick down this street. Go around the AI car. Oh, now we're getting it. We are just throwing it down here. Definitely getting the hang of it. I do love this 180SX. Go between that. Lemondry the poles. What? We got it? Oh. Come on. You can't tell me that that was not sick. As we do that, we just biff it into the wall. See if we can't follow this Ferrari. Apparently, he must follow us. Basically, doing the little Gymkhana freestyle here in the city. We're going to be able to hold that, we are. We're going to be up here. We're going to surround that. But we're not doing it too bad at all. I thought we were going to do a lot worse, but we're definitely getting it. Until that, we've got Jack BX91 ripping his 4-5-8. Just see a smoke trail. I don't know where he went. We're just going to go this way. Like I said, definitely having a lot of fun with this. This is like street drifting major for the win. Just that. Roast tires. I could probably just session here in the streets for hours, especially with the drift cam. Oh, we were working our way through these poles. I have no idea how we pulled that off. But we did. Oh, my Lord. That was intense. Sorry, I kind of focus on those poles there.  Do a little more. Bye. We're going to hit that one, so we're going to bail out of that one. 4-5-8 up there trying to do it too. Clutch in, thrilling a break. This is as we do a little donut. I was going to do a little donut around this, but it was a lot bigger than I thought. Donuts, I feel, are going to be very weird in this camera. Ow. That's a train. So if you guys like seeing basically freestyle drifting here on Forza Horizon 4, make sure you tap that like button and subscribe. I do appreciate all the support. As always, I thank you guys for coming and watching all these videos and everything as they come out. Make sure you tap the subscribe, tap the like button, hit that bell notification if you want to get the videos right away. It does help me out in YouTube analysis for videos for other people seeing it. So make sure you follow me on Instagram and Twitter. I'll just find the description box below. When cut, don't cut. It's my co-driver. And I had a lot of fun doing this. No joke. A little old street sesh. So as always, I'd like to thank you guys for watching. I'm EvilRabbit. I will see you guys next time. Hard initiation. All tap. That would have been sweet.


So, this is lecture 20, right, ok. So, right now we are looking at the ISI case when you cannot assume that your channel is ideal anymore and Nyquist criteria is not satisfied by the received pulse spectrum. So, you will have ISI necessarily, ok. So, I am going to once again draw this picture, ok. So, you have a symbol sequence SK. So, you usually think of this as a finite sequence say length L symbol sequence, ok. So, the transmitter first thing you do is send it through a transmit filter, ok.  You should do upconversion, right. So, imagine G of t is I mean S of k can be complex.  So, instead of doing all that we do a passband equivalent picture where we simply say we have a complex baseband channel C of t, ok. So, this is complex baseband, ok. And then noise gets added to this, ok. Once again this is actually the complex baseband equivalent of noise, ok. So, all these things are there, one can do that, alright. So, here this is your received signal R of t, ok. So, we initially started off by saying what do you do with R of t? We thought of doing a minimum distance receiver from there we were able to see that convolving with h star of minus t seems like a very natural thing to do and sampling at sample rate. And then we also later on saw that if you want to do an optimal projection onto an orthonormal basis also you can convolve with h star of minus t, then sample at symbol rate and then do a discrete time filter, ok. So, that is the those are all equivalent ways of thinking about it and I am going to do that next, ok. So, the first operation that you would want to do is to filter with h star of minus t, what is h of t? And sample at signal rate, symbol rate, ok. So, this immediately means c of t should be known at the receiver, ok. Otherwise you cannot hope to implement h star of minus t at the receiver, ok. So, typically the way I have written it down it looks like h star of minus t if at all it is implemented in the receiver it is going to be in analog, ok. So, you never do things like that, how do you do it? Oversample R of t, sample it to a very large amount and then you do even the filtering by h star of minus t in digital, ok. So, you never do these things in analog because you cannot control the filter shape and all that very easily, right. So, you do k t. Of course, once again the sampling here there might be a delay to accommodate for various things, ok. So, you do that you get y k, ok. And this y k has a very simple description the way I wrote it down, ok. So, y k will actually be sk convolved with the autocorrelation of h, ok. So, it has is i on both sides, ok. y k will depend on sk sk minus 1 sk plus 1 sk minus 2 sk plus 2 all these things in a symmetric way rho h of k, ok. So, it seemed like one thing to do to get rid of the anti-causal is i was to filter with 1 by gamma square m star of 1 by z star. How did I get that? So, you look at the spectrum of rho h of k, ok. So, you see rho h of k is actually what it is, it is h of t convolved with h star of minus t sampled at k t, ok. So, that is rho h of k. You do a Fourier transform discrete time Fourier transform of course, you get sh of e bar j 2 pi f t, ok, which would be a valid power spectral density for which you can do spectral factorization, ok. You would get spectral factorization to get a minimum phase m, right, ok. So, this actually corresponds to m k which is monic causal and minimum phase, loosely minimum phase. I am going to simply say minimum phase. Remember that the zeros can be on the unit circle, ok. So, what was gamma square? Gamma square if you write it down will work out to exp 1 by 2 pi integral minus pi to pi log sh of e power j theta d theta, ok. So, this is the formula for gamma square, ok. So, it will work out like that, ok. So, if your sh of z is rational then you can do the minimum phase factorization in a simple way, ok. So, you simply take all the poles and zeros in m of z inside the unit circle and then half the zeros on the unit circle into m of z and the remaining will automatically come in m star of 1 by z star because sh of e power j 2 pi f t is real and non-negative on the unit circle, ok. So, those things will work out. And gamma square you can choose suitably. Here the gamma square will work out to this formula, all right. So, if you see all this then you notice that you can do a filtering here with 1 by gamma square m star of e power j 2 pi f t, ok. So, however small I write it it ends up over shooting. So, I am going to simply say m star of 1 by z star, ok. So, hopefully hopefully it is clear to people m star of 1 by z star works out to this, this filter and out of this filter you get z k, ok. So, we saw that this entire operation filtering by h star of minus t sampling and then filtering with 1 by gamma square m star of 1 by z star was nothing but doing an orthonormal projection, right on the signal space corresponding to the signal received at r of t, ok. The signal component r of t defines the signal space on that signal space if you do an orthonormal projection you would be doing the exact same thing. But the difference from what we did before was z of k will still contain i s i you cannot get rid of i s i because your pulse does not satisfy the Nyquist data in general. So, it cannot get rid of the i s i in total.  So, z of k, z k you can show this is very important, z k you can show is s k convolved with m k plus n k. Remember all these guys are complex now. See s k is complex, m k is complex, n k is also complex, ok. So, each component of n k will be i i d normal it means 0 and variance n naught by 2 gamma square, ok, right. Each in each dimension n of k will be like this, ok. So, that is the orthonormal projection you project into project with an orthonormal basis every dimension will be normal with 0 mean and variance equal to the variance that have that was there before, ok. Initially you might think the variance is different, but after you filter with h star of minus t you have a gamma square entering the no actually it becomes colored and then you have a 1 by gamma square. So, that will multiply it out and you will get it. So, but those constants are irrelevant do not worry about this n naught by 2 gamma square, ok. Only in an exam problem it those things will become relevant, ok.  You measure it in practice and then you know what your SNR is, ok. So, nothing it is not too significant there, ok. So, this model is very very crucial. So, what people do usually is they say they will denote, ok. So, you remember what we did for the non ISI case. We went from a received transmit constellation directly to a received constellation from SK to SK plus noise, ok. So, we went there directly. So, now people usually bunch up this whole thing together and get what is called a discrete time model for ISI, ok. You go from SK to ZK directly and the only thing that happens from SK to ZK is what? Filtering by MK and addition of noise which is IID 0 mean some variance, ok. So, that is the discrete time ISI AWGN model and this is very very popular in practice, ok. So, you will see most people when they do simulation studies and in fact, even in practice you always work with this model, ok. You do not look at the whole system in complete detail. If your channel is known at the receiver you can equivalently work with this model, ok. So, where S of K goes through MZ, MZ is what? Monic, Causal, loosely minimum phase, ok. So, MK is that and what you get out is going to be SK convolved, ok. You have to add noise, sorry, followed by addition of noise which is NK to get ZK which is SK convolved with MK plus MK, ok. So, this guy is IID normal in each dimension, ok. So, with may 0 mean and variance sigma square and this is the BK, ok, which is received value, received symbol value, signal value. In the non-ISI case, we simply had S of K plus noise. Now, you cannot do that. You will have S of K convolved with MK, ok, right. MK is Causal and all that. So, this BK can be written in a very nice form, ok. So, you can write it as K equals 0 to infinity, M, ok, L I think, L equals 0 to infinity. I want to write it so that I get, sorry, let me write it this way, ML, S, K minus L, ok. I can do this because I know MK is Causal. So, only the positive things will come, ok. So, you notice B of 0 contains components from S of 0 and something before and we did not transmit anything before S of 0. So, nothing else will come, ok. B of 1 will contain S of 1 and then S 0 as well. B of 2 will contain some component from S 2, S 1 as well as S 0, ok. So, of course, you cannot observe B of K directly. You can observe only B of K plus noise, ok. So, that is the only thing you observe, but B of K is the received signal value, ok. So, now it is possible to draw things like received constellations, ok. So, a transmit constellation was nice S of K and say some BPSK, QPSK or 16 QAM. Your received constellation, if you plot the BK, will no longer be the same thing. So, it will be something else. We will try and we will try that exercise soon enough, ok. We will see some examples where you plot the received constellation and it will be different, ok. But one thing I know definitely is the noise that gets added to BK is IID Gaussian 0 mean, ok. So, that those are all nice things to do which we can use in our detector, ok. So, that is the overall idea. So, most simulations that people do for ISI is AWGN. It will always be in this model. Nobody is going to simulate that whole thing with G of t and C of t and H star of my machine. It is not necessary because the whole thing is equivalent to a discrete time model and a discrete time model is much easier to simulate in software but, right. So, you just and it is all symbol rate, ok. So, you do not need to do too much of, do not need to have too much memory and all. So, this is how people usually simulate, ok. Any questions on how this model was derived, ok. And the crucial assumption of course is you know H of t, yeah, right. If you do not know H of t, you cannot really do it with the receipt. So, if you do not do that, then your model will be different. We will see those cases later. For now, we will assume it is known at the receipt, ok. Any questions, any comments, it is ok. Everything is fine. So, the next thing I want to do is to look at, ok. So, I want to look at the detector, but before that, let me just quickly do a few more things that is common in practice when people think of simulating such things. So, what is usually done is when you are thinking of a channel M of z, you want to normalize M of z so that the energy is 1 in M of z, ok. So, there is a good reason why you want to do it. So, typically normalize such that summation over k mod mk squared equals 1, ok. So, the reason why you want to normalize this is now energy in sk will be equal to energy in what? Bk, ok. So, once you normalize this Mk to have unit energy, there is no energy artificially being introduced in your model, ok. And that will cause some confusion because if you for instance scale by 10 to get from sk to Bk, it is not right, ok. So, it is those noises not getting scaled. It is just scaling this and that does not cause all kinds of confusion, ok. So, in your model. So, it is always good to normalize your channel in the ISI model to unit energy and when you do not have to worry about differences in transmit constellation and receive constellation energy. It is all normalized and it is nice. So, you do that, ok. So, this will make this will make the. So, if I do this one property of M of z might be lost, what is that property? By the normalization. Monic. Monic is the only thing that will be lost. Other things will not be lost, ok. So, one by scaling nothing will happen, but the monic property might be lost, ok. So, that is the only thing to keep in mind. So, this is done to make energy of sk equal to energy of Bk, ok. So, one thing you can do for instance if you are worried about SNR, how do you define SNR now, ok. Energy in s divided by 2 times sigma square. The reason why I am doing 2 is what? Because I want to account for both dimensions. When I do energy in s, I am going to find energy in 2 dimensions. So, I want to divide by noise energy in 2 dimensions. But even if you do not put that 2, the only thing that will happen is your entire curve will shift by 3 dB left or right. But if you plot uncoded versus coded or something, comparisons will still be valid as long as you stick to the same model, ok. So, it is not a big deal, but it is usually there is a 2 factor, ok. So, SNR is defined as in your model E s divided by 2 sigma square, ok. So, if you want to think of it as N0 by 2 gamma square, then it will become N0 by gamma square in the denominator. So, gamma also enters the picture if you want to go back to the continuous time model. But like I said, it is not too important to worry about those kind of these things. All right. So, now let us see a few examples of this discrete time model and how things work out. The reason why I am doing it is I have to solve the next problem, ok. So, I have not solved the receiver completely. What is the next step? Detection, right. So, if I have got the z case, I have to now detect my s case, and it is not the same as before. I cannot do independent detection for each k because I have got ISI, ok. So, I have to detect for the whole thing together. So, how do I do the detection is the next question. For that we have to understand the discrete time model very well, ok. So, for that we are going to see a few examples and then I will give you a nice view of the discrete time model which will help us move to a detect, ok. So, that is the kind of road map roughly. So, let us see.  First example I am going to take for mz is 1 by root 2 minus 1 by root 2 z inverse, ok. So, in fact I might even violate the minimum phase criteria, ok. So, when I pick mz, ok. So, that is because I do not want to think of minimum phase when I come up with examples. I want to be able to just quickly come up with examples. In reality, you might have a minimum phase thing, ok. So, I will just quickly come up with examples. Do not shout at me if it is not minimum phase, ok. So, now what is, ok. So, couple of other things I need to define, ok.  This guy is my what I have called as b k, which is the received signal value, ok, after the just the ISI, ok. So, this is nice. So, if I want to now get a hold of the received constellation and all that, I have to fix the transmit constellation, ok. So, my simple example, first time I will take x to b b ps k, ok. So, which is the simplest example one can take, ok. So, if it is b ps k, what will be the received constellation, ok. I am drawing two axes, I actually do not need two axes, it is only one dimension, it is all real. But what will be the values when the received constellation? Yeah. So, there is a 1 by root 2 floating around. So, just be careful about that. So, s k and s k minus 1 can take 4 different possibilities. So, technically there should be 4 different points in your received constellation, but some of them might overlap with each other, ok. So, less than or equal to 4 points that I know for sure, ok. So, after that is just a question of substituting the different possibilities and finding different b k's. If I substitute both to be equal to 1 1, what will I get? 0, ok. So, I get 0 as 1 point. If I substitute both to be minus 1, what do I get? 0 again. So, that is an overlap, but that need not necessarily happen in general, for a constellation it can happen. What are the other two values? root 2 and minus root 2, right. Am I right? So, that will be your kind of received constellation for each k, but remember each k is not independent, right. Do you agree with me? If I give you the constellation or if I give you the actual occurrence of b k at k, the next occurrence is closely controlled. It cannot be anything else that you want, ok. So, keep that in mind. So, it is all each k it is not independent and the transmit side it is independent, right. I do a constellation and for each k I pick a point independently from the constellation. Here the receiver I do not do that, I only pick the transmit and the receiver comes forward, ok. So, that is important when I draw the constellation remember that it is not independent for each k, ok. All right. So, let us do a slightly more complicated case. We will do the constellation, the resistance, transmit constellation being QPSK, ok. So, I want you to think for a while, consider all possibilities and draw the received constellation. It is a good exercise. I will give you some clarity about what is going on. First of all, how many points do you expect? 16 points, right. So, those are my points. I have how many points do I have? Put 9 points, am I right? And that is where they occur, ok. So, each of these guys, the squares will be 1 by root 2 plus or minus 1 plus or minus j, ok. So, those are the 4 points, all right. So, one interesting exercise which is a standard quiz question once again is to find energy of a particular received constellation at 1 k, ok. So, how do you find energy now? So, remember all these points will not occur with equal probability, ok. So, you have to be careful. SK occurs with equal probability. For each of these points, you have to compute probability. For instance, in the BPSK case, it is easy to figure out what the probabilities are. What are the probabilities? Yeah, the probability half here, 1 by 4 here, 1 by 4 here. So, you do that and compute, you will get your energy back again to be 1, same as before, ok. So, but you have to do this computation. So, you have to compute the probability at which, with which each point might occur. It is not uniform now, ok, because of the way in which my SK is worked out, all right. So, this is an interesting exercise and you can see this exercise is going to get complicated when, what happens? When will this exercise begin to get complicated? There are 2 things. When there are more taps, ok. When you have more taps in your M of Z, this is going to get complicated and then the second possibility is when there are more symbols in your transmit constellation, ok. So, in fact, you can get an exact relationship for the maximum number of points in your received constellation in terms of these 2 things, ok. So, you can show if you have a mu tap M of Z. So, what do I mean by a mu tap M of Z? M0, M1 Z inverse, M mu Z power minus mu, ok. So, this is what I mean by saying mu tap. So, when I say one tap, it is not a scalar multiple, ok. It is actually one ISA. So, if you want to say multiplication by a constant, I will say 0 tap, ok. So, it is a constant thing, ok. So, remember this notation, this can get confusing because different people use different convention here. My convention here when I say mu tap is mu plus 1 order, ok. So, you have got M0 through M mu, ok. So, remember that, ok. So, if you have this and if your transmit constellation is X, then number of points in received constellation is less than or equal to what? Yeah, size of X power mu, ok. So, it grows exponentially in mu, ok. So, that is a bit of a problem, ok. You have to be worried about this problem because if you want to do detection on the ZK and if M of Z has too many taps, you have to worry about too many points in your constellation, mu plus 1, ok. Is that a mu plus 1? Ok, yeah, that is a mu plus 1, ok. So, I have to worry about too many points in my received constellation and it is going to get quickly complicated, ok. So, that is something that you have to keep in mind and today everybody wants very high spectral efficiency. So, people are using 64 QAM, 32 QAM without any problem. So, at least 16 QAM is being used. So, when you have 16 QAM and then you have and you want a signal very fast, which means you have to face a lot of ISI, ok. And you have 10 taps, you are pretty much done. You cannot even hope for doing any such a keeping track of any such received constellation, ok. So, those are problems and we have to address those problems as we go along. For now, I will assume it is manageable and talk about the ideal detector, ok. So, I will talk about the ideal detector first and we will quickly see the ideal detector is not that implementable as it becomes more complicated and then we will worry about other things, ok. So, I want to do one more example, just to show you that this can get a little bit more painful and it is also an example which I am going to have around for the other things as we go along. So, this is the second example. Once again, I have no idea if this is a minimum face thing or not, but I know it is monic and it is not. I mean it is FIR as in it is causal and it is normalized, ok. So, that is the only thing I care about. I do not know if it is minimum face or not, ok. So, that is my M of Z, ok. So, you can see it is normalized, ok. Suppose I say X is BPSK, ok. So, I want you to plot the received constellation, ok. So, the same exercise if you try with BPSK, it will get even more complicated and ugly, but it is possible to do it, ok. So, you will get many more points, but BPSK is not too bad, ok. One can do it, what would you get, ok. So, there are 8 possibilities 1 plus 1 by root 2, ok. And then minus 1 minus 1 by root 2, ok. And then 1 by root 2 minus 1 by root 2, any other possibility, ok. So, minus 1 plus 1 by root 2, 1 minus 1 by root 2, any other possibility, ok. That is it, ok. The only 6 points, ok, right. So, one can plot these things, ok. So, you can do 1 by root 2 is what, 0.7, right. So, it is closer to 1 than 1 minus 1 by root 2. So, you will have, you will have points like this, ok. So, I do that, 6 points. And probabilities you can compute, you can compute the received energy and all that, ok. So, you try for QPSK, it becomes a bit more of a headache, ok. So, it is difficult to do these things and keep track of these things, ok. But simulations you can do very fast and quickly generate this, ok. So, all right. So, I am thinking I mean I want to return your answer scripts and discuss some things there as well. So, I think I am going to stop here for this class. I will return your quiz answer sheets and then we will pick up from here in the next class.


Hey guys, this is Nate, aka the Foot Account, and welcome back to the channel. We're talking about team of the group stage today, the promotion that is coming on Friday in FIFA 21 Ultimate Team. This is the promotion that we expected to come right after Black Friday, the first weekend in December with matchday five ending this week. We had Tuesday and Wednesday of this week with Champions League matches, matchday five, and then we have got Europa League today on Thursday as well. So we're going to talk about that promotion, what we know already, what we can possibly expect, look at a prediction or two, and also talk about the weekly rewards market today. Talk about the PlayStation 5 because there are people getting on to the next-gen console version or the next-gen release of FIFA, it seems, like all the new adaptive triggers and all sorts of gameplay. The new PS5 gameplay for FIFA 21, I'm on the PS4 still. I do not have a PS5, have not been able to snipe one yet on the 59th minute per se, but we're going to take a look at some of the stuff that could be happening with that as well and look at the new team of the week, possibly the market rising with rewards today and another base icon SBC. This is getting very party-bag SBC-esque of EA Sports. They continue to release these base icon upgrades, you know, every couple of days. This one's only out for two days. It's going to expire before the promo starts on this Friday, which is very interesting. Very, very interesting. They're doing it this way. It's almost, again, like I mentioned, kind of like they used to do the party-bag SBCs last year during, like, what was that, like, foot-birth day before team of the season, maybe even during team of the season and stuff like that. But again, let's go to the big thing on tap for today and that is the info we got on Wednesday about team of the group stage. Now, I tweeted this graphic out. This is from EA. This is the actual graphic. This is the actual car design, which I believe is exactly the same as last year. And when I tweeted this out today, you know, I said the recycled car design, that's kind of the way that EA works. It seems a lot of the car designs for the Champions League, road to the finals, man of the matches and Europa League get reused. I don't know if there's anything like they just designed it once. They don't want to mess with it. But this is the car design. It almost looks exactly the same as last year. I would go out on a limb and say it is exactly the same for the most part. Yeah, I think it looks exactly the same. But we will be seeing this team probably an updated loading screen today on Thursday. I would expect to see probably three cards today on Thursday with a few hints. Last year, I wasn't expecting this. Today, yesterday on Wednesday, I was expecting this screen to come out today on Thursday, but the EA dropped it a day early because they want to promo their new stuff that is coming out. Of course, this is the team from last year. I don't know if you guys remember this team of the tournament group stage. We had Messi, De Bruyne, Kane, Lewa stacked squad last year, big time players in packs. This year, it's not really looking like it's going to be that quality unless EA just juices up cards and puts cards into packs, not even based on the performance just to actually sell packs. We'll talk about that today as well. Then we had a couple Europa League items. Even in FIFA 19, we had a really solid team in the group stage. I don't know if you guys remember this last year, but Messi right around this time as well. A lot of the market started dropping off because of this promotion and how packable these team of the group stage cards were, but also because of the player of the month Messi, SBC, was coming out last year during this timeframe in FIFA as well. I don't know if we're going to get as good of a team of the group stage squad this year as we did last year. Here is a prediction coming in on Twitter from UncleFoot and a couple other guys. I'm going to leave this link to the prediction in the description. One thing I'm going to be very interested to see this year is, does EA throw in a guy like Messi or does EA throw in a guy like maybe a Ronaldo or a big top tier player? Do they throw in Bruno Fernandez and Marcus Rashford or just one of those two? Do they throw in De Bruyne to try to make this squad look more appealing than most people because so far with the players that have been playing well in the Champions League, I don't know who EA is going to put into this. Of course, Holland probably has to get in. Rashford could get in. Bruno could get in. Guys like Coman, Timo Werner, Joe Gomez or Possibilities. Morata has been playing well. You know, guys like Jota and Ferran Torres who have ones to watch cards that would get upgraded if they were to get a new item here because this is performance-based. Those ones to watch items would get upgraded. That's one thing to watch out for. A lot of those OTWs are already inflated. I think Playa is 100% getting one. He's got like five or six goals and three assists or something like that. That was through matchday four. It's just this year a team of the group stage is not looking like it's going to be that good, but I'm sure EA is going to throw in some cards to make it look good. They're going to throw in a few players here to sell packs and to do the business as you know, but that's kind of interesting to me. Other thing that's sort of interesting to me as we look at some past promo teams that we've had already this year, like Road to the Final Cards or even like record breakers when they released the record breakers, right? They only have been doing a full squad of 11 at one time. Record breakers are probably the best example for this. They just release 11 special cards per week. Like they do one week with 11 and if it's a two week promo, they go 11 cards and then 11 cards. They can't really do that with team of the group stage because right, I mean, I guess they could, but right after this we have foot mist. So this is probably going to be just a one week promo like it always is. Hopefully they put more than 11 cards in packs. Maybe at least just like they did last year with a sizable promo team like this. That's what I will hope for because if it's just 11 cards in packs, that's kind of a dud in my opinion. I would like more. I would like a little bit more. So give us a full squad EA. Well, probably again, like I mentioned, get more to this loading screen today. Probably they'll start to give us the hints, right? Put a nation on there, put some stats, some ratings, and then maybe some like coordinates on the actual loading screen itself to get us guessing, to get us predicting and all that sort of stuff. Now with week and league rewards today, what does this mean? Since we know now week and league rewards are in, you know, probably not too long or even have already passed after you're opening up this video to watch it. But with week and league rewards today, we got a lazy sale on walk-ins. Let's freaking go. I think not a lot of people are going to be opening their packs. There's a lot of people that are saving packs right now. I think they're going to continue saving them. And I do think that still makes the market rise up. This market has a lot of coins right now. As you saw my transfer list, I've got some Hyunmin's sons. I bought these, those cards for around 70,000 coins or under today. And right now he's kind of still in the same range. I'm going to pick up that sum of the hunter for 70K because I feel like gold cards and just meta stuff overall is going to rise this week on the market. I do feel like the market is still going to rise because without packs being opened up, you have less supply to the market in terms of those cards that maybe you wanted to buy that are in packs have less supply. But there's still demand because people still buy teams on Thursdays for their week and league starts up on Friday. So I still think you're going to see a market rise today in a lot of areas. Now the new team of the week that came out today as well, I do want to show you guys this over on the Twitter. This was the new team of the week that came out today. Romagnoli, Mendy, Aguilar, Rafinha is one that I want to look at and Griezmann are two cards that I want to look at from this week's team of the week. Now these are cards that we kind of knew were coming because they were technically leaked last night before the actual team came out. They were leaked in concepts. Griezmann is dope, Mendy is dope, Rafinha is dope, but this team of the week might be one of the worst team of the week we have ever seen in FIFA Ultimate team history. It's so bad. And of course guys like De Bruyne and Marez didn't get in. We did get a Mendy inform, but that is making people think we might get a team of the group stage De Bruyne. That's why you saw De Bruyne in that prediction. I think that seems realistic. These are going to be cards that you could watch today at rewards, possibly flip. Rafinha has a lot of height because of his links. Basically, this is like this is like an informed Lucas type card. I don't even know. Like if you compared this guy to Gold Lucas Mora, how he compares, but I'm going to be completely honest. It's probably pretty, pretty close. 83 rated Lucas Mora is 11,000 coins. This card is 144,000 coins and Lucas Mora has more total stats or no, sorry, less total stats, less in games, but they're very, very close. The physicality is the biggest difference and then passing Rafinha has a little bit more plus two pace plus two dribbling. So, or plus two dribbling on Lucas. So these are basically the same card and there are 130k difference. I feel like this Rafinha is very overpriced if I'm being honest with you at the moment, but a lot of these cards will drop. Griezmann's low, man. I think this is very low for Griezmann. If you do want to look at cards today during rewards, people that have elite rewards and up are going to, are not going to hold these cards because or hold those packs, the tradable team of the week packs, there's no reason for them to hold those. So, I would definitely keep an eye on some of these informs today at rewards because they might drop and then rebound after the rewards time period as people go out and try and buy those for their teams. I would watch Mendy, Griezmann, possibly Aspas, Leltaro Martinez and Rafinha as those cards. And I guess you could even watch Romagnoli as well. Actually, this is one thing I want to check. How did Donoruma do today as a record breaker as a link investment? Because this guy was already up a lot. Did he continue to go or did he get, okay, he's about the same price, 89K after the Romagnoli came out. So maybe Donoruma goes up a little bit today after rewards with people getting Romagnoli as a red item. But yeah, man, the market today wasn't really impacted that much by this icon SPC.  We saw some of the 85s and 86s go up because of another base icon upgrade. I wonder if people are just waiting on this though.  I thought it said one day remaining, man. Hey, yo, where's the base icon upgrade? Are there two of them out right now? Or the two base icon? One day 15 hours. There are two of them out because I did not do the second one. And there's also, there's also this new one that came out today. So that is my bad. I thought this was only after two days. It's out for four days. So I do feel like some people might not be doing this right now, along with my original thought process, because they might think that, okay, we've got a promo coming this weekend. We've got some promo packs, possibly SPC fodder is going to drop a little bit. That's not, you know, that could happen for sure. But there's so many SPCs that are out right now. Of course, we are waiting on that Joao Felix Player of the Month and a lot of that stuff. Other SPCs that could be coming with Team of the Group stage could possibly coming out as well. It's something to keep an eye on. And we'll have more Player of the Months coming soon too. Bundesliga, Premier League, League on Player of the Months the next few days, actually probably next week or so. But there's just a decent amount of SPCs that are out right now. But I don't think a lot of people did that icon SPC today right away. I think they're kind of waiting on it. And maybe with rewards today, seeing what they're going to get and stuff like that. So the market didn't really crash per se. There are still some deals out on the market. If you do want to take a look through some past Team of the Weeks today before rewards, there are some cards that are still kind of low. Some stuff has trickled upwards. This Mars is up another 10k. Gretzgr is up. Tishara is up. Some of these cards have continued to rebound. Now after more Champions League action today, some of these cards are still very low. Draxler is about the same after PSG winning today against Manu. Let me check Rashford really fast. Where is he at? Rashford is 9.58. So he is down after the loss today. Klosterman is down for Leipzig. A lot of these to Kari is still kind of low. Davies is still chilling at 5.50. So some of those cards, some of the rule breakers have rebounded a bit too. Quadrado still 2.30. Jimenez is up. Royce is up. Tishara is up. So keeping on some of these cards as well after rewards, I do think they'll rise. They're just rare. They're out of packs and they should rise. I'm really curious about these. 5.30 for Vardy. 3.20 for Sancho. Really curious to see, and Bape's back at 3.2. I'm really curious to see what these cards kind of do today with this market and the current situation of the game right now. But I do not think that Team of the Group stage and the loading screen is really going to stop people from buying teams just yet. It might stop the buyback a little bit, but I don't feel like there's a lot of reason for panic, especially since we had an icon as PC today. I really don't feel like there's a lot of big content that we could get on Thursday. I don't feel like there's a lot of big content that we could get on Thursday today and foot. I feel like it's mostly the stuff that came yesterday on Wednesday. There's actually a lot that was released. The Team of the Week, a couple new SBCs, the base icon, the loading screen. There's a lot of stuff that happened on Wednesday for FIFA Ultimate Team. Thursday I think should be a bit quieter, updated loading screen, maybe some sort of SBC or something like that. I wouldn't expect too much. There is a lot of hype going around though right now about the PlayStation 5. This is one thing I do want to show you over here on a foot bin actually is that there are, first of all, there's a lot of people talking on Twitter right now about the PlayStation 5 and the graphics and how good it looks. This picture, this is from Matt HD Gamer on Twitter. This picture of Allison. Look at those graphics, man. That's a bit scruffy of a beard on Allison, but look at the graphics and the hair, the face, the sweat, the eyes, that's crazy. Crazy, crazy graphics. If you have a PlayStation 5, your graphics are looking insane right now. I really don't know too much about that because I'm still rocking the PlayStation 4. I'll get a PS5 eventually, but at least it's not going to happen right at this moment. If you do though, make sure you do update because I think it's an update. You have to download or something like that. People are figuring out how to do that. Check on other, maybe like on Twitter, there's probably ways to do that if you're having some issues because I did see people having issues. Now, these are also cards that people are clicking around on their seeing. It was on a couple pictures, screenshots taken from NextGen consoles about these cards right here. These are like gold cards with the same exact stats, but they have a different design. These are very interesting-looking cards. I don't actually know if these are cards that are going to come out if it's a new card design or if it's just something to promo NextGen because the whole NextGen promo with either EA has been doing has been kind of like the red and blue, so I don't know what these cards are exactly. I feel like they're not going to be released in the game, but I don't honestly know what these are, man. I think they're just kind of like maybe some sort of like NextGen. Maybe they're going to be loans or something like that. They'll give you loans. I don't know. I really do not know, but these are just gold cards with kind of a weird... It's just like UCL cards. Honestly, it's like another UCL card is what these are for PS5 or Xbox Series X. I really do not know if these are. Hopefully, we get some more information on that today, but that's also stuff that could be coming out on Friday with Team of the Groups Age. It could be a massive Friday, boys. We could have Team of the Groups Age this Friday. NextGen officially being out December 4th. That was like the official drop date for EA Sports. Also, Icon Swaps. It is early December and it could be Icon Swaps time, so we'll see if we get any more information on that today on Thursday as well. But until then, good luck with your reds and rewards. If you're opening packs, good luck. If you're saving, hopefully, your saving ends up treating you well. If you're watching the market today, hopefully, we get a nice little market rise on a lot of cards and icons out of packs, informs a lot of the stuff that I've been keeping an eye on. I do feel like it goes up today. I do. Where's this Bruno at? Where's my guy Bruno at right now? Because he's been fluctuating between like $375, $380, and over $400K today. This guy fluctuates a ton, man. Right now, he's $390. Looks like this Bruno's like $390. There's a bunch listed at $420 right here. This is somebody investing for Thursday Flip. See this? We got $1, $2, $3, $4, $5, $6. $6. Bruno's all listed at the same exact time, close to the same price. That is somebody who did a little Thursday Flip investment on ADA Bruno. I like that a lot. But if you guys enjoyed this video and you're hyped for PS5, FIFA gameplay, or team of the group stage, thumbs up on the video, comment down below if you have any questions, and, of course, subscribe to the channel if you're new. Good luck again on your rewards today, and let's make some coins with a nice little market rise. It's been Nate the Foot Accountant, and I will catch you guys later. Peace out.