Hi, I'm Zor. Welcome to InDesign Education. I would like to spend some time analyzing mathematics behind frequency modulation. So basically I call this lecture frequency modulation equation. It's a mathematical expression of how exactly the frequency modulated signal looks like. This lecture is part of the course called Physics 14. It's presented on Unisor.com. I suggest you to watch this lecture from this website. You have to go to Unisor.com. Then there is a course, Physics 14, the part of the course which this lecture is part of. It's called Waves and among the waves there is a topic radio. So this lecture is part of that topic radio. Okay, now why? Because every lecture has notes, very detailed notes on the website. So if you find it, let's say on YouTube, you will not be able to read it. And notes are written as a textbook. On the same website you will have Math 14's prerequisite course, which contains all the math which I am using today and in many other lectures. Math is an absolute necessity for people who study physics. Now there are many problems for those people who would like to take exams. They can actually take exams as many times as they want. Now there is a certain educational functionality in the website, which means if you are studying under somebody's supervision, then that somebody can enroll you in certain courses, take a look at your exams, etc.  There are no ads, no strings attached. You don't even have to sign in if you don't want to this type of supervised studying. Okay, back to frequency modulation. Well, first of all, what do we try to accomplish by frequency modulation? Just as a reminder, there is an amplitude modulation. So if you have a high frequency carrier signal and some kind of a sound wave, whatever sound wave is, and sound wave is basically the changes of the air pressure and it has much lower waving than the high frequency signals. Then we are changing the amplitude of the high frequency in sync with the way how the sound wave signal goes, how the air pressure goes, which means the result would be higher amplitude of oscillation in this case than lower here, high here again, lower here again. So this new signal is an amplitude modulated signal which represents this particular curve of the sound wave, of the air pressure basically. Okay, so that's amplitude and it's kind of easily understood. Frequency modulation is a little bit more obscure. So again, let me tell what we want to do. For instance, this is a curve which represents the air pressure as a function of time. Now, how our high frequency modulation should look like if you would like to modulate frequency, not the amplitude. So the amplitude should remain exactly the same in the high frequency oscillation. But whenever there is a higher pressure, frequency must be greater, which means our curve should go tightly in this case. Now here, we have a lower air pressure and our oscillation should go with the same amplitude but a little bit less frequently. Then again, we have high frequency here and lower frequency here. So again, if you can look at this as a spring actually, now the spring will be tighter here and it will be not as tight in cases of the low pressure. Again, tighter here and the greater the intensity of the sound, the greater the air pressure, the tighter should be these loops of the spring. So that's how it goes. Now that's the purpose. And today, I would like to express this particular curve, how it looks mathematically based on how this curve looks. The modulating signal is this one. This is a function of time. So the function of time is a modulating signal. This is basically air pressure as a function of time at some particular point in space, let's say where our microphone is, because the microphone is converging this air pressure into electric signal, let's say current in some circuit. And that current should somehow overlap with this current, which represents the current in the main carrier LC circuit. Remember, LC is inductor capacitor circuit which produces oscillating current. We spoke about this. So this is the main carrier circuit and it has certain main base frequency, depending on L and C. Omega 0 is equal to 1 over square root of L, C. So that's all we know. So there is something like a main frequency. The main LC circuit of a transmitter is supposed to run on. Now, this modulating signal should change the main frequency. I mean, without the modulating signal, our frequency, whatever we are transmitting, should look uniformly, with the same angular frequency, this is angular frequency, all the time as a function of time. So it basically would be... So this would be the main signal. So it's a sinusoidal signal, constant amplitude, constant frequency, without any modulation. My purpose is... Now, and this is function of time, obviously. This is unmodulating signals, unmodulating oscillations of this circuit. Now, my purpose right now to come up with another formula, which basically gives me modulating oscillation, modulated oscillations of this main circuit. So the frequency should be changed based on modulating signal. So how this particular new formula, mathematical formula would look like, which represents the function of current in the LC circuit based on time and modulating signal. So, again, all I know is that with a higher modulating signal, I have to have higher frequency. The question is, how can I represent it in formula? So that's what we're going to talk about today. Now, before everything, I would like to step aside a little bit and talk about frequency. I know some people have a little problem with understanding this concept as far as the frequency is concerned, because there is some differentiation, integration involved, etc. So what is frequency? Now, we used to think about frequency as either just regular frequency or angular frequency. Now, regular frequency f is number of cycles per time. So if you have something which is just oscillating, which we are saying like five oscillations per second, it means that every second there are five full circles of oscillation. Every two seconds, we have 10. Every 20 seconds, we have 100. Now, that's regular frequency. Now, when we are talking about frequency, we very often express our function as this type of equation. And whenever we are talking about full cycle, so the frequency is how many cycles per, how many seconds or how many cycles per second actually, we are talking about a period of the function cosine. So the full period and the function looks like this. So full period is, let's say from here to here or from here to here, whatever, doesn't really matter. So how many full periods per second this particular function makes? That's the regular frequency. Now, we know that this function has period 2 pi. Now, every period of the function cosine has length 2 pi. Now, what's the period of this function? Well, the period of this function is 2 pi divided by omega 0. That's the period. Now, this 2 pi comes out as kind of an inconvenience. And what people actually did, they were considering this type of function as a representation of certain mechanical movement. Now, what's the mechanical movement? If you have a circle and you imagine your point here, and let's say this circle has a radius A. So this point is at x-coordinate A. And then it starts moving, uniformly moving. Now, what is its x-coordinate? Well, if the radius is A, the x-coordinate is A times cosine of this angle. This angle, considered as a function of time, is basically the argument to cosine. And if our movement is uniform, now, uniform movement means that phi of t, the angle of rotation is equal to some kind of a constant by time. This is a uniform rotation. Now, in this particular case, for the uniform rotation, we see that our x-coordinate is exactly what we actually have to have. So let's talk about oscillations as a result, basically of some kind of a point, uniformly rotating, as I was just describing, on a radius A with a frequency, with a speed. Actually, now it's angular speed. You see, there is a very direct analogy between the distance and speed in kinematics and this angle of rotation and so-called angular frequency. This coefficient is called angular frequency, basically. In this electronic, radial, et cetera, kind of a physics type of things. It's a direct analogy. So this is the distance. This is a uniform constant speed. This is time. So speed times time would equal to distance. In this particular case, the distance is measured as an angle in the region. That's why whenever we have a full circle, we have two pi regions, right? A radian, two pi regions. That's why the period of function, cosine in this particular case, is equal to two pi. Now, if the point is rotating faster, this is faster. The period will be proportionally smaller, right? So if the regular cosine of T has the period two pi, then if I multiply the speed of rotation by factor omega zero, my period will be reduced, obviously. So whenever we are talking about this equation as representing, let's say, radio waves, we definitely can model it as a rotation of a point around a circle of radius A with a speed. I'm using the word speed. Actually, it's angular speed. Omega zero, radians per second. So there is a direct analogy between kinematics, distance and speed terminology, and this radio electronics when we are talking about angular frequency and amplitude. Now, if there is a direct analogy, let's just push this analogy a little bit further. So, we obviously know this. Now, this is good because for uniform rotation it works and it fits perfectly. Now, we know, again, back to kinematics, that distance can actually be the result of multiplication of speed by time. For uniform movement along the straight line with a constant speed. But, again, a little further in studying the mechanics, we were actually studying something like accelerated movement or, in theory, any kind of a movement with variable speed. And what is speed if you consider that you know the distance as a function of time? Well, let's go back to our mechanics, actually. And the first derivative of the distance by time is actually a speed as a function of time. This is a momentary speed, speed at any particular moment of time t. Why is it derivative? Because, obviously, if you take some kind of a moment of time t and then the next moment of time t plus a little increment, you can consider that during this very little time interval the speed is not actually changing. And your speed can be considered during the whole interval as being equal to v of t, the speed at this particular moment because these are very, very close to each other moments. And now, at the same time, we know that function of time, function distance of time at this particular moment t plus delta t has value t plus delta t. And the previous moment, distance was like this. So this is increment of the distance. And if you divide it by time, which passed from one moment to another, you will have an average speed during this very small amount of time. And whenever we will reduce the amount of time, this time increment, we will make these two events very, very close to each other. So this will be smaller and smaller and this will be smaller and smaller. And in the limit, we will have something which is called the first derivative. And that's why this is goes to v of t as delta t goes to zero. So that's why this formula, which implies that if our rotation is not uniform but has a changing frequency, we have absolutely analogous relationship between angle of rotation and instantaneous, first derivative of angle of rotation is instantaneous angular speed. Exactly the same. So for uniform movement, yes, if this is a function, the first derivative of this function is omega zero. This is a simple linear function and that's uniform movement. But if the movement is not uniform, if our point is moving faster at one particular time and then slower and then faster and then slower, etc., then the instantaneous angular frequency is actually instantaneous angular speed. It's just a tradition that radio engineers are calling it frequency. It's basically angular speed. Angular speed depends on angular rotation and angle of rotation in this particular fashion. In exactly the same fashion as distance and speed are related to each other. Because angular rotation is actually angular distance and the angular speed is basically how fast we are moving. This is very important to understand. Now, and this is a very simple concept which is actually no different than kinematics concept of distance and speed in case of non-uniform movement. So this is the same. This and this are the same. Okay, great. Now, from the terminological standpoint, angle of rotation is called a phase. And again, it should not be understood in any different way than just an angle of rotation. So what's the phase of some particular oscillation? Well, if oscillation is uniform, then it's basically an angle by which the point managed to turn during certain time t. So in this particular case, if the point is here, then this is an angle. So phase is a function of time which represents basically the angle by which the point managed to turn during the time t. So phase is a function of time. Phase is angle of rotation by the time from zero to some time t. That's what phase actually is. And again, it should not be understood in any other sense, but just the angular distance by which our point managed to turn. And as usually, x-coordinate of the point, we are considering as our main variable which we are studying. We are always studying the x-coordinate of the point. And the point is rotating around this particular radius a in this particular case. Now, if we know this, we know from angle of rotation, we know how to determine the instantaneous speed of rotation or angular frequency if you would like. So angular frequency and angular frequency, this is our omega t. So these are basically radio-electronic kind of terminology. The angle of rotation and angular speed are more mechanical, so to speak, language. But they mean exactly the same. And the relationship should be exactly the same. The same relationship as between distance and speed. We have between phase and angular frequency. Now, there is a small misunderstanding because sometimes the word frequency is used in angular sense and sometimes in the sense of how many periods per second. Now, number of periods per second, but if the period is actually 2 pi divided by omega, then the frequency is equal to how many periods per seconds each period is this. So frequency is equal to basically omega divided by 2 pi, which is basically 1 over 2. So this is, sometimes people are mixing this frequency with this frequency. Now, this frequency is number of periods per second. This is number of radians per second. And since each period is 2 pi radians, that's why we have this relationship. And sometimes in formulas you have omega, but sometimes instead of omega you have 2 pi f, 2 pi f instead of omega. Formules are exactly the same. It's just what exactly we are talking about frequency, frequency in number of periods per seconds or number of radians per seconds. It's just two different scales, but they mean absolutely the same. And the difference is in this multiplier 2 pi. Now, I will use omega because it's just simpler. You don't have to write 2 pi. Okay, so. And there is one more very important piece about frequency, angular frequency. When I'm saying frequency, it means angular frequency from this. And from very simple mathematics. You know if there is a function and there is a first derivative of this function. Well, from function we can get first derivative. Can we get, from first derivative, can we get the main function? Well, very simple. Well, in pure mathematics it's supposed to be minus infinity instead of zero. In physics, we don't deal with minus infinity, we are talking about movement. So the amount, the angle of rotation by the time t is basically integral. Integral is a reverse of differentiation. So this is differentiation, this is integration. And that would give me angle of rotation from moment of time t0 to moment of time t. Well, I shouldn't use the letter t in both cases because that's kind of confusing. Let's just use Greek letter tau. It's just a variable of integration, doesn't really matter. So this is an elementary mass, which you kind of must know. And that's why there is a mass for genes, course, prerequisite course on the same website. So how to do differentiation and how to do integration should be of no problem. In elementary cases, I'm not talking about some high complexity things. So, so far this is sufficient for us to talk about frequency modulation. And here's how. Now, whenever we are talking about frequency modulation, we are talking about not a constant frequency. It's not a mega zero, but it will be frequency which depends on time. That's very important because sometimes when my modulation, modulating signal is stronger, I have to have higher frequency. Whenever it's weaker, I have to have a lower frequency. So basically what I would like to talk about is a modulated, modulated frequency. This modulated frequency obviously should depend on main frequency of our circuit, which produces main base frequency on which basically our transmitter is transmitting signal, plus something which depends on the strength of the modulating signal. So if my modulating signal is some kind of a function of t, I have to add this component. Usually it's added with some kind of a multiplier lambda called modulating index. This is a contribution. This index actually kind of controls the contribution of the input signal to frequency. And basically that's it. I mean that's how our frequency modulation is done. We are adding to the main frequency on which this particular transmitter is tuned in. We are adding something which depends on the modulating signal. So this is the sound, let's say. Now, it has certain limits of strength. Now, our widths of the band around this particular frequency should be obviously restricted because there are some other transmitters which would like to also transmit some information. So for each transmitting radio station we give the certain band of frequencies. And we were talking about this. For FM radio it's from 88 megahertz to 108 megahertz, divided into 100 pieces. And within each 100 we will have some kind of central frequency and frequency around it to compensate this particular thing. So we should use the modulating index to narrow down this particular thing. So what happens now is basically pure mathematics which you definitely are familiar from whatever I was talking before. If you know this, how can you recreate our main equation? Well, again, let's go back to main equation. We started with this unmodulating signal. Now we would like to have the modulating signal. Now, our current in the LC circuit is a cosine. Now, instead of this, I will use phi of t. In uniform case, angular speed times t is angle of rotation. In a non-uniform, we have a different speed, but we can recreate this thing very simply. Modulated angle of rotation as a function of t is integral of 1 of t, omega modulated as a function of tau. Let's use a different letter, d tau. This is a derivative. This is the angle of rotation, angular distance. So this is angular speed, angular distance, and the distance can be derived from speed using simple integration. So let's use this here. And what do we see now? We see the phi modulated at t is equal to integral from 0 to t. Omega 0 plus lambda modulating signal of tau. Sorry about that again. d tau equals... Well, if you multiply this by this, you will have one component, which is this, plus another component, which is lambda goes outside m tau d tau, which is equal to... Now, this is a simple integral, which is omega times t. And this is as it is. I don't want to do anything about this, from which I... So the current modulated as a function of t is equal to a cosine modulated f, which is omega t plus lambda integral from 0 to t, m of tau d tau. That's the final formula of modulated signal. And what I did in the notes for this lecture, I had an example. I had a function m of tau as some of... I don't remember the numbers, but it's something like, you know, 3 times cosine 2t plus cosine t or something like this. I took this as m of t as a combination of two different oscillations. Maybe there are two musical instruments.  One is, let's say, louder, another is softer. This is producing higher pitch and this is lower pitch. So it's like an orchestra from two different instruments. Whatever it is, it doesn't really matter. I could take any function here. It doesn't really matter whether it's trigonometric or not trigonometric. It's just usually when we are talking about sound, we have a combination of many different harmonic oscillations, and not so harmonic, but in any case some kind of oscillations. So that's why I took this as m of tau. This is m. And then I basically integrate it. I mean, it's easy to integrate cosine. You know, the derivative of sine is a cosine, integral of cosine is a sine, and the derivative of sine is cosine. So it's very easy to integrate. And I come up with a formula and draw the graph. So the graph of m of t. So I draw this graph and this graph. And it appears actually exactly, if this is the sound, my frequency was much more intense here and much less intense here. Then more intense here and less intense. And the amplitude was the same. So I had these two graphs presented in notes for this lecture. And you can take a look at this. Well, that's it. My purpose was to come up with this formula and draw a particular example how exactly this frequency modulation actually looks like. Now, in my example, as a base frequency, I did not use a very high frequency because otherwise my graph would not be really easily decipherable when it's too high frequency. You don't really see the difference in frequencies if it's really too high. So I had exactly the number where you see that sometimes it's rarer and sometimes it's more frequent waves of the resulting graph. In theory, this frequency is significantly greater and it allows to... You see, this frequency is from 88 MHz. So it's 88 MHz of oscillations per second. That's high. Okay. So it allows to accommodate any kind of a sound, even high-fi. So little deviations maybe from some smoothness which basically represents some particularity of the sound can be accommodated using a very high frequency as long as we basically know how to produce this signal and how to receive it and convert back frequency oscillation, frequency modulation into some kind of a sound on the receiver side. And basically I don't know all the details but as far as I know this frequency modulated signal after it's received is converted somehow into amplitude changes because eventually we have to really produce the sound through some kind of a speaker and that's why we need the amplitude. So there is some kind of a conversion but that's beyond the scope of this particular course. It's more for radio engineers. So if you will be a specialist in this particular area you will know exactly how it's done, how to transmit this signal and how to receive it on the receiver side. Okay, that's it. I suggest you to read the notes for this lecture including the graph which is presented there. Actually click on the right button on the graph and open it up in a new tab on your browser so it will be bigger and much more decipherable. Well, that's it. Thank you very much and good luck.


These are the days where I do not like to report on the news because the things that we're going to talk about today Are not very positive especially with what's going on with the SEC is they're really bringing some maximum pain And when we talk about the issues that the SEC brought against these different Influencers and companies and everything else. I want you to think about the far-reaching implications that it has to do with in crypto blockchain gaming and web 3 in general and And then you can understand why America is really done with crypto. So first things first, let's take a look So today there was a nice little tweet I always find it interesting that the SEC likes to tweet out like, you know, they've got nothing else to do But this is a tweet today. I said today we charged impact theory LLC a media and entertainment company headquartered in LA with conducting an unregistered offering of crypto assets securities in the form of NFTs, let me say that again Crypto assets securities in the form of NFTs impact 30 raised 30 million from hundreds of investors And then it goes and talks about without registration investors of all types are deprived of the proper the protections Afforded them by the robust disclosures and other safeguards long provided by a securities loss. Look I'm not going to get into the fact that's you know These disclosures and other safeguards really protect people because I'm sure they do But you know what didn't protect anybody was FTX Voyager Celsius Block 5 when you had the opportunity and sat down with with SPF. I find that very odd but it is what it is and When the SEC brings charges and of course They've already settled Impact theory has settled with them. They agreed to pay. I think it was six million dollars Correct me in the comment section and impact theory As far as I've taken a look at and correct me in the comment section, but impact theory LLC They're a media company out of LA and this is with Tom bill you I think I always I always say is rain wrong great guy Great channel a lot of information But they just did NFTs and they sold it off and now they're saying that this is in on rudder security now I'm sure That they probably tried to go to the SEC or maybe they didn't I don't know but the same thing has been happening with Binance with Coinbase with Everybody that you can pretty much think of with ripple as they've gone to talk with the SEC and sat down with them And it's impossible to register with them because they just keep saying they don't give them the actual information they need to actually registered Perfectly or at all and of course we have this issue. So now if you think about NFTs Think about NFTs think about that in general If the SEC is going to crack down on NFTs and they're gonna say this is definitely security What does that mean for everything that we try to put on the blockchain as far as NFTs? That could go from something as as massive as real estate as we try to Securitize things and actually put The different properties onto the blockchain via an NFT. So those businesses are just gone Now think about what I think is gonna lead the next bull run Web 3 gaming or as I call it block gaming a lot of those games have to do with NFTs So if NFTs are all securities that means that every single game out there that uses NFTs are going to have to go and register with the SEC if they want to play ball in America And the thing is a lot of these companies are gonna say themselves. Why the heck are we dealing with Americans? When I try to go over then I try to register with the SEC and I cannot do these things I am hindering my business. I cannot grow anything. This is not the land of opportunity This is a lot of persecution and I'm not gonna be able to go through this whole process And I'm actually dwindling and I'm dying on the vine by saying that Crypto and digital assets are now dead in America. There is no reason for a company to launch here in America whatsoever, and they're gonna go away Ourselves we're launching a product ourselves. It is a blockchain game web 3 we're gonna launch a web 2 first But every lawyer that we've talked to so far has said you will not Launch in America and we were hemming and hawing. Oh, well, maybe good runs of things But there is not a chance. There's not a show of snowballs chance in hell We will ever do anything in America as long as Gary Gens on the SEC is cracking down and does not give a clear pathway Having said that don't worry. I'll get to some good news. I'm not all doom and gloom So then there's this this is from Andrew founder of x3 pretty good Twitter account a link in the description This is updated shouldn't come as a surprise that the SEC SEC staff have their site set on a collection of crypto influencers This is from the source. I don't know whose source is but whatever if they created a token and Benefited in a meaningful way Expect there to be consequences Same thing with NFTs. I believe if there is our influencers out there That created NFT think about all the ones that have done this think about all the companies that have done this Think of all the individual people that have done this how many of those people are now in the sites of the SEC a lot of them Same source low hanging fruit. That's easy to track and prosecute Now you can let your imagination run wild with all the people that have actually done this But I got to tell you if they're gonna come after NFTs That's everybody now Fortunately, I didn't get into that craze. I did drop a coin called tomato coin. I don't know if anybody remembers that It was a joke and it was free. So I think I'm on the clear on this one But it is quite concerning Taking a look at at what's happening and then also this was from well, this was from all coin daily great channel check out and They say the SEC versus Richard Hart case is separate November 28 2023 and then there was a correction Cory coasts Cory coasts crypto coins is it's a conference call not a case this is from Hex and pulse chain and things like that and he says no, no, no, it's just a conference call I gotta tell you I don't care if it's a conference call or or what but The wheels of justice do move slow and I'm not saying that Richard Hart here is guilty I'm just saying if you're getting a call from the SEC, it's usually not a good thing Moving forward so that is what's going on and again, I hate to be the bearer of bad news But when I see something like this happen the only way a Through a there is no there is no around this the only way through this is to do exactly what ripple did this is something I I called for gosh over a year ago, and I said the SEC will never let up never is It is the understanding that they will just keep pushing forward and the only way to go through with this is to sue the SEC People say that's ridiculous. Why would anybody do that? So here we go. It's gonna pick us off I think it was Benjamin Franklin that said We should either hang together or we'll all hang separately meaning there's power in numbers and The SEC even though they lost that case Partially with ripple they're still making waves and we'll see how it all works out But I gotta tell you the only way through this is a long Difficult process in the courts in America while the entire crypto industry goes off-site offshore Which there's well they should Especially with the Asian countries as they embrace crypto India and all the different places parts of Europe, Switzerland When all this happens, we're gonna be stuck in these court cases against the SEC It's gonna cost tens of millions of dollars People are gonna lose a good amount of money because Gary is protecting us harder And unfortunately there's only one way to do that and that is through the SEC Let me just think about that in the comment section It's not all that nice Hey, there is some good stuff. How would you like a tangent wallet? So I on Twitter. Oh shoot, you know what I didn't do this follow me on Twitter at news asset and We did a deep dive into the tangent wall. I think it's pretty good. I like it so far and It's not a sponsored post. They didn't pay me anything or anything like that. I just picked up a Tangent wallet because I was concerned about my nana ledger wall I think we all are in one way shape or another, right? So I just thought well if I diverse them in my portfolio I might as well diverse my cold storage devices and it's super simple So I'm just gonna give away a couple of wallets. Just follow me on Twitter Comment rate we the post follow tangent and me and then I'm gonna we're gonna do the drawing Livestream on Thursday.  It's actually August 31st That'll be this this Thursday. So there's a little good news and then also I just want to start a little education part here and I want to get everybody's feedback But I tweeted this out and I just asked the question was would you consider this a good example of good tokenomics? Of something positive that you would get into so this is tokenomics If you go to coingecko.com, there's a little tab of it You can click on which says tokenomics you can find most of this stuff But I just want to ask the question like people do you know tokenomics doesn't make sense to you So look at this one. This is an allocation If you had a crowd sale meaning that it is public and at eighty three point three percent is available to the public But sixteen point seven percent Goes to the foundation and early contributors Would you consider this good tokenomics and then here's the unlock schedule? Or supply schedule and you can see that this one. I'm not going to tell you what it is But it started in 2015 and it's already unlocked as of 2022 The total is 120 million tokens. That's important But it can go up to infinity So would you consider this a good example of good tokenomics and I can tell you it is or what it is I'll talk about that in tomorrow's video, but just put that in the comment section. Let me know what you think and then lastly Lastly I am obsessed with this tool that Ben's got at the end of the cryptoverse and it's it's the DCA tool because So we had Jerry on Jerry v. Hall not make jaggers girlfriend Jerry Hall On the show yesterday. We did another live stream and usually I don't do live streams during the day I thought this doesn't mean a lot of questions. We'll get to those in a bit, but It was Aristotle or Plato and he asked the question. He said hey Rob, why do you guys talk about you know putting so much money in when a lot of us are you know living paycheck to paycheck? It's kind of disrespectful. Well, he didn't say disrespectful He said it's you know, it's kind of like you really aren't taking into account all your your subscribers I thought that's pretty true and I showed him The DCA tool and I said, you know Like when I got out of the military, I mean there was I mean for like six months or so I was working at UPS at the airport and I was making ten dollars and fifty cents an hour. I thought I was balling and But I realized pretty quickly that you know the apartment crappy apartment I lived in and then of course food and then insurance and car and gas and everything else It really adds up so it's not you know much to invest So I said, you know Aristotle Plato. I understand so I showed him just this this example And I said look, this is this is Cardano. I Said, let's just say You've you're gonna and this is of course the past it doesn't mean this is gonna be the exact same thing going forward However, if you believe in Cardano and a different ecosystem, then this is a play for you Not a financial advice not your dad all that good stuff But I showed him I go look if you're going let's say Cardano.  Whoa, that's not right Let's go 20 bucks a week. That's what I showed him Yeah, 100 bucks a day might be steep for some people. I get it. Let's just say 20 bucks a week if you did that and you started on December 14 20 because that's as far back as this one goes for Ben on on the site. I said if you did that So first of all, there's two ways to look at it There's this thing called lump sum if you had 1100 bucks because if you did if you went and invested 20 bucks a week From 2018 to 2020 the total investment would be one thousand one hundred dollars if you take one thousand one hundred dollars and you lump sum it and Dollar cost average from 2018 thousand twenty one three years doing that This is what you'd have in Cardano, and if you were to sold the top good luck. I can't do it But maybe you can But your lump sum would have been worth ninety nine thousand dollars But if you would have had eleven hundred bucks back then But if you don't and you live in paycheck to paycheck, I get it But if you dollar cost average you would had sixty four thousand dollars And I was that's pretty good quite honestly Depending on what Gary says if it's a security or whatever And of course you didn't do so hot. Maybe you got it down here. Maybe you sold on October 2021 Well, it's silly. You still put in 1100 bucks. You stopped on 2020 That's forty eight thousand dollars For a dollar cost averaging or if you lump sum seventy four thousand and I thought about it even further. I go well, okay Let's do this Let's take a look at Bitcoin Damn, I did it again. Not daily. Let's do Bitcoin 20 bucks a week Because it's you know Cardano's back then it was pretty risky back then now I think it's not as risky, but some people will disagree with me whatever That's what makes the channel great, but let's say that I do the same thing in January 1st 2018 When Bitcoin was coming off its highs remember on January 1st 2018 the price was 14,000 Next week it was almost 17,000 and back then in 2017 December I think the high was like nineteen thousand nine hundred dollars something like that So let's say you did this again You put 20 bucks a week into Bitcoin and but you stopped on in January 1st 2020 That's twenty one hundred dollars. You would have put in over that whole time if you could have lump summed it You've been doing pretty good actually in November you would have put you would have had twenty thousand dollars Which is crazy because it's that's the dollar cost average if you lump summed it back to your You actually would have had half of that So now people and like if this I want you guys to sign up and play around with this tool So you know what I'm talking about not and you can see and you can you can use a bunch of different assets I mean all these assets all these assets and see what it is and come away with a conclusion what's best for you I took it even further. I said, okay, how about this? Let's say I lump summed it Again twenty one hundred dollars roughly and I started it because we're all talking about the four-year cycles right four-year cycles everybody talks about it I believe in him too So there's a theory That if we have the four-year cycles We're coming up into the Bitcoin halving year, which is next year of 2024, right? So the last Bitcoin halving year was back in 2020 actually it was a May 12 I think it was now we're coming like April 17. So my arm there So let's say that you'd lump summed it. Let's say you saved all this time You're gonna lump sum and you would have done it in the last halving year. What would that look like? What would your gains would have been? Well, if you had a lump summed Over here on January 1st 2020 the last Bitcoin halving year And if you would have had it you would have topped out at 19,000 dollars It's not bad. I mean doing like, you know a 10x just for hanging around for Not even what is a year and a half. It's pretty good quite honestly But then I thought about this because that's not the most opportune time January 1st 2020 Let's take a look at the last cycles The the last cycle low Well, I don't know if we're in the low right now, but the last cycle low, did you know it was it was an 84% drop? It's always happened this way November 2013 was the high $1,100 and the cycle low was January 2015. It was an 85% drop the next cycle 2017 The high was 19,665 the low was 3200 on 2018 it was an 84% drop That's why I still think we have ways to go because the lowest that we've gone so far is 77% I could be wrong But it's it's happened the last eight years one of the last so going forward But let's just say this let's take the most opportune time and Lump sum on the lowest point that we could have gotten in the last eight years or something like that six years five years genius five six years $3,200 that was the cost of Bitcoin. So let's come over here and let's say we put 20 bucks a week And we started on December 16 2018 That would have been $1,100 if we were bought for 55 weeks just 20 bucks a week, right? We could have lump summed if we had 1100 bucks Back in December 17 2018 when it was the all-time low $3,200. What would you have gotten? Well Your lump sum would have been 22,000 but your dollar cost average of an 11,861 roughly half Roughly half But that's the perfect time to lump sum. Can you hit that every time? I Don't know if you can I'm not that good. So let's just take it. Let's just do this instead of starting So that's what we got, right? But what if we would have screwed up and we said, you know what? I'm gonna lump sum on November Guess what if you missed that perfect down point your lump sum is worth 12,530 your DCA's worth 13 13,537. Let's not cherry-pick. Let's go back another month October Roughly the same thing. Let's go back another month. I don't know September 1st. How are we doing? Dollar cost average just beat the lump sum. Let's go back one more month. You see where I'm going with this, right? You'll never know where it is Lumps some could work out pretty well, but I'm just telling you that as time goes on there are gains to be made But it's up to you to decide what you want to do and what's best for you and your family So let me know in the comment section what you think about that me personally. I just do dynamic DCA Where time and the risk bands and I just kind of I doubt I buy the same stuff every day So it doesn't really matter to me. I increase or decrease just a little bit Right now we're stuck right around here. So it's like the same thing every day, which is boring But I mean, I think I'll be handsomely rewarded in 2024 2025 206 who knows and then lastly if you're looking for that tool Did you know That it is free to use that tool. I just showed you there's a link in the description Into the cryptiverse this light plan right here.  I just want to tell you how Crazy I think this this this is right here and the reason why I think it's crazy is because they're doing one wallet So there was a big speculation about this wallet number three And of course we talked about this like a couple weeks ago I think it was where everybody thought it was black rock I didn't want to cover it because I was like I don't really know if that's true and then turn out to be Robin Hood Great. So Robin Hood now has the third largest Bitcoin wallet with over three billion in Bitcoin And you can see it right here if you go to bit info charts calm and you click on the Bitcoin rich list It'll show you Bitcoin address one two. Let's I'll show you It'll show you Bitcoin address one two three and the first one is Binance the second one is bit for next and the third one is apparently Robin Hood and You can see all this what they've done they got over three billion dollars and what they did What Robin Hood did was they they had a bunch of different wallets. They said ah, whatever throw into one wallet. I Got to tell you like does anybody feel like that's a kind of crazy if you just do like one wallets like me personally I have three nano ledgers and now I just got the tangent. There's three. There's three cards there Like I'm just I'm like one wallet for three billion I mean, I guess if you have your seed phrase or you have a backup for the cards I guess so but I find it just fascinating that That's You know people Robin are like, you know what throw in a wallet three billion whatever and that's it so everybody That's it for today. I'm sorry. It wasn't better news about what's going on especially with all the NFTs and the things that I think that America's done with crypto because of one guy and his Belief of what's going on But that's what we got today. So look if you gotta take off take off Thanks for showing up. I appreciate you like today's video give it a thumbs up consider subscribing Everything was very time-sensitive especially moving into the Bitcoin having an April


Hi everyone, happy Sunday. I'm Joe for jaspyscasebrakes.com with our final filler pack that we have to do to unlock that six-spot giveaway of the last six spots in that high-end baseball mixer the three-boxer that's on the site So let's do this jumbo pack really quick big. Thanks to everybody here for making this happen There's all the teams right there. Let's roll it randomize it two and one three times So we'll do a different dice roll for the giveaway part, but for names and teams in this quick pack three times Two and three Two and third and final time for the teams All right, I'm not gonna read off all these names, but here's the first half of the list right here And here's the second half of the list right there. Let's just go ahead and print and rip There's the final print out right here very nice pot off the presses no trade windows and Or extremely short-trained windows and these filler breaks Crazy or no autographs or anything like that No, nothing too crazy But what's crazy is gonna be those spots that were given away. So let's grab everybody's names again Let's Get them into the into a new list right here. There's some new dice Let's roll it randomize it two and a six this time eight times top six after eight good luck one two three four five six Seven and good luck eighth and final time. So top six so from seven on down not happy But I appreciate everybody giving this a shot. Thank you Sad times for them, but happy times for the top six congrats to Alan Alan Kevin Alan again. Wow Alan and Rosario Alan Murdock needs to buy a lottery ticket four out of the six spots. That's pretty nice There you go. Hey, that's the way it turns out sometimes. I'm Joe for jasperjasebricks.com Congrats again. We'll see you next time for that. We'll see you in the next video for this for the break itself Jasper's case breaks.com


Hello friends and visitors and welcome to Monet Cafe. I've missed you guys. I've not uploaded a video for a while because I've had some company and some craziness in my life but I thought today I'd give a little short and sweet video and Give you guys some information on pastel storage techniques and tips I know I've had a few people inquire about that on some of my other videos So I thought I'd give a quick little studio Tour of how I store my pastels and I thought what a perfect time to do this because this is the dreaded day That I am deciding to put all of my pastels away that I've used for other projects Now I've already put a lot of them away This is just a couple of little pallets that I have laid out all my miscellaneous pastels to start putting away now I'm going to show you my system of pastel storage, but there's multiple ways that you can store pastels. I Particularly love the storage system of pastel artist Richard McKinley And I learned a lot from a pastel artist friend of mine named Deborah Seacour as to how she Arranges her pastels and so there's various different ways you can do this and a lot of it's just your own personal preference But one thing I would highly recommend because I talk so much about the importance of value You may notice that most pastel artists do store their pastels in a way that Makes it easy to identify the value of a color now for example this happens to be my drawer system and It is my my blues and my purples and I happen to think I probably have a smaller selection of pastel To create the amount of pastel work. I have over the years than any other artist That's a bold claim perhaps not, but I know I don't have the largest selection I see pastel artists that have so many pastels and I'm a little bit envious but but I'm happy for those artists at the same time and So I'm going to show you kind of how my little system works. I have I found this at a little Home craft store type of place and I have things on top of this now But this is a neat little let me move this out of the way This is a neat little drawer system now. I have my blue drawer out already on my drawing table But what I do is I have this drawer system to where the top ones are the blues that I have The next ones ends are my greens. I'm going to sit this down so I can pull my my drawers out and show you and This is my greens and again, I have not put a lot of these away And they've gotten a little out of order I would typically have my my lighter values back here and they've just gotten out of whack So I have my my warmer greens on one side and my cooler greens on the other side And they go from light to dark typically again some things are out of order a little bit but then I have my My next drawer are my yellows and my oranges. I mean oranges and reds and then my next drawer are my pinks and in the pink and earthy brown family in here and The last drawer is for neutrals and I haven't yet got things going there I just have my blacks and whites in there. So as you can see, I don't have a Tremendously large selection of pastels now. I do have some pastel pencils I do have a selection of a harder pastels that's not in that drawer and you may have seen in my videos sometimes for under paintings I'll use these water-soluble wax pastels, but that's pretty much it for my pastels So that should be pretty encouraging For others to know that you can you know over a just a little bit of time I know they're expensive, but you can accumulate enough to actually Create some pretty good works of art and I wanted to show too. This was the first system that I used It's just these boxes it's called Degas Artists pastel box and it's just a box that has Some I think I may have put this in here. I think I did I'm not sure if it comes with the foam in there, but I did the same as my drawer system putting my pastels in there Now I use these boxes Just for moving them around or when I'm working on a painting or something now this next little piece of equipment here or drawer is actually a modification I did out of a little transportable drawing tablet or box that you can take with you when you're traveling and I took the drawer part that fits under here and I just loaded up with pastels that would be Adequate for going on a trip and doing some pastel work And this on here was a little art less than I did in watercolor with their color caterpillars showing how to blend colors That's watercolor not pastel however, um, I also wanted to point out too For um beginners These are an intermediate. These are a couple of really good pastel books that I used When I first got started, this is the pastel book by bill Crevy And this one is pastel painting techniques This one here shows you more techniques and ways to use pastels And there's just a ton of information in here on different techniques. And again, all these things become your own personal little way that you work in pastels and Everybody develops their own little interesting techniques and ways that is unique to you This one here is just lots of information on pastels in general Some some techniques are in here too, but a lot of it is just on education about pastels So those are a couple of really good resources. Again, this little video was just short and sweet Um, hopefully giving you some good information about how to keep your pastels Um, one other little quick tip, uh, I've developed. Um, just kind of recently It's just to keep a newsprint wherever I'm working or up on my easel when I'm working So that you may notice these pastels get kind of dirty sometimes this one's this one's pretty dirty here And so I can just rub it pretty quickly and it's clean There's all kinds of different pastel cleaning techniques as well But that's just one that works pretty good for me. So anyway, I hope you guys learned something from this quick little tutorial or demo or instruction video and, uh, happy painting to all of my friends I'm really enjoying having you guys here with me and hopefully I'll be back to my regular upload schedule And I hope to upload at least a video a week. So thank you subscribers and thank you new visitors and happy painting. Bye


Hey this is Brett and this 2015 Dodge Challenger Hellcat with the brass monkey wheels is stock number 14410Z. I am here at Summit Audemotive in Fond du Lac, Wisconsin. You're new and used Dodge Challenger and sports car headquarters. This 2015 Dodge Challenger Hellcat has the 6.2L supercharged V8 Hemi engine. It's paired up the six-speed manual transmission. It puts out 707 horsepower with the red key. We do have two red keys for this car and one black key. This car has been fully safety-danned and inspected by our service shop. It has a fresh oil and filter change. All the fluids have been checked and topped off and this car is 100% ready to go. Probably one of the cleanest used Hellcats we have ever had on our lot. I'm going to go all the way around in this video inside. Start it up, take a look under the hood, show you all the options and give you the most accurate representation that I can of the vehicle. White Ivory Tri-coat Pearl is the color I shoot all my videos in 4K. If you like the video, subscribe to the YouTube channel, click the bell notifications, get updates on the videos I do each and every day, and stay current on our ever-changing and vast sports car inventory here at Summit Audemotive so you do not miss out on gems like this one. This one comes with the 20-inch Brass Monkey wheels. No scuffs, no scrapes on those wheels, even the little Hellcat Velostem cover on there. It comes with the Brembo brakes, these slotted rotors. Once again, no scuffs, no scrapes, and it comes with the Pirelli P0 Summer 27540 ZR20 tires. I'd say these tires have right around half, maybe a little bit more than half the tread left on them. Front fender is exceptionally clean on this car, no dents or dings on there. Front bumper and lower valance are all in excellent shape as well. This car, the front bumper has never been drilled into. The lower valance is in excellent condition. No major scuffs on there. It has the HID headlamps, the LED running lights. I'm going to turn those on at the end of the video so you can see just how bright they are. This one comes with my favorite hood on the Challengers, the single cove induction and then the heat extraction on both sides. Look at how nice that hood is, no dents, no dings. Paint is in excellent shape. Passengers side, front fender, absolutely perfect as well. And the passengers side front wheel, no major scuffs or scrapes on there. Very nice. White Ivory Tri-coat Pearl has a lot of metal flake in it, a lot of pearl as you'd expect from the name. Always a little tricky to get it to focus. But as you can see just all that metal flake in there, really a cool color. There you go. You can see just how nice that clear coat is. Really, really nice. And as you go down this side, much of the same. Take note of how clean the body is, how reflective and mirror-like that paint is. I didn't see any dents, I didn't see any dings. I take these HD videos so if you're far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle, you can see the car, hear the car and have confidence in what you're looking at before you even get here. So when you do get here or if you get the car shipped to you, you know exactly what you're going to be getting so that when you see the car in person, there's absolutely no surprises. You can make a smart informed buying decision from wherever you're at. Now if this video helps you make that buying decision, let your salesman know that you saw the video, that it was helpful and that Brett said to you. Back wheels in excellent shape. You get the Brembo brakes back here as well. And the back tires have just about as much tread as the front tires. Coming around to the back of the vehicle, rear bumper is absolutely perfect. You get the backup parking sensors, the kind of blacked out dual rear exhaust, LED tail lamps. That plastic there is in nice shape. You get the deck lid spoiler. That is in nice shape and the deck lid itself. Very, very clean. We do have the guards for the front lower valence. They come with the car. This one also has the factory Harman Kardon subwoofers, tire inflator kit, and that's where your battery is located. Those seats do fold down for extra storage. You can see the shocks are doing a nice job holding that trunk lid up. Something you always want to check for on these challengers from this vintage. Down the driver's side just as clean as that passenger's side. No dents, no dings. Very, very clean. And for full disclosure, this back wheel just as nice as the rest. Door edge is in very nice condition as well. It does have the enter and go system. Down the rest of the side of the door. I didn't see any dents on there. Heated mirrors, blind spot monitoring. Inside the Hellcat package gives you the black leather with the red Alcantara suede. No rips, no tears on these seats. SRT stitched into the backrest. Even the bolster has almost no wear on it. Power driver's seat with lumbar, factory floor mats, power pedals, auto headlamps, power tilt, and telescopic steering wheel. Harman Kardon premium sound system power windows locks and mirrors. You get the suede insert on the door there. Take a quick look at the back seats. They are trimmed out the same way. Smells very clean inside this car. No rips or tears back there. I don't believe this car has ever been smoked in. We'll hop inside, check out the miles, the radio, and everything that this one has to offer before we start it up. You get the Hellcat logo on there. 6,137 miles on this car. You get the digital speedometer, time display. You can change that to a compass, mileage, whatever you want to change that to. It's all configurable. This one comes with the heated leather wrap steering wheel, cruise controls on the right, Bluetooth and information center controls on the left. You also get the flat bottom steering wheel on there. Notice the machine metal finish look around the radio and dash. That's in really nice condition. You get the 8.4 3C radio, AM FM and Sirius XM radio capabilities. You have your heated and cooled seat buttons as well as your heated steering wheel controls.  This one, there's highway 41 so you know that that is working properly. Another thing you always want to check for on the vintage, this vintage of Challenger is that the navigation system is working. This one is working, so that is great. Let's see if we can put it in reverse. Show you the backup camera here. There we go. Our car has to be on for that to work. Oh, there we go. And that is working nicely as well. You get all your different apps on here. It does have SRT apps, performance pages, all that good stuff. They do take a second to load so while they're loading push button start, down here you have more tactile volume tune and climate controls. You get that machine metal looking center console there as well. Here is the black key. Like I said, we do have two red keys to go along with that. Six speed manual transmission and like I said, these apps, you get the performance pages, all the apps right there, SRT drive modes and all that good stuff and then see if it'll go to the performance pages. Like I said, they take a second to load. I must not have hit the button before. Anyways, passenger side format and seat excellent condition as well. No rips, no tears. Like I said, it smells very clean in here. The headliner is absolutely perfect. No rips or tears up there. Map lights, home link buttons for your garage door security systems and lane systems, 911 and assist buttons in the mirror. And here are your performance pages. You get timers on here as well as the different gauges, the G-Force, the engine and the first time you load this up, it always takes a second. So you got your current timers, you have your gauges on here, gauges to G-Force and then what the engine's doing. All right, we're gonna start it up and then we're gonna take a look under the hood, listen to the exhaust and we'll be all set to go check out all those HID lights in the front as well. Starts right up, no check engine lights or anything like that. I do have the parking brake on right now so if I pull that off you can see that goes away. But we're gonna leave that on. There is your engine, you can see the boost pressure there and if I give it a little gas, you can see the horsepower and torque changes on there. All right, let's go take a look under the hood, listen to that exhaust a little bit, we'll be all set to go. I love how the Hellcat sound, definitely my favorite sports car exhaust. Love those LED tail lamps as well. I would personally like to thank you for checking out the video today and hopefully from this HD video you've been able to verify the quality condition and cleanliness of this car all the way around inside and out and like I said this is definitely one of the cleanest Hellcats we've ever had on the U-side. HID headlamps, LED running lights and under the hood you get the 6.2 liter supercharged V8 Hemi engine, 707 horsepower engine base very clean, runs very smooth and once again this car has been fully safe and Inspector by our service shop has a fresh oil and filter change all the fluids have been checked and topped off. There is the emission sticker, I mean look at how clean it is under this hood. Just really really nice example of a 2015 Hellcat. I don't think you will find a cleaner one and this car is 100% ready to go. I would highly recommend it from a quality and condition standpoint. I'd ship this one to California, Texas, New York, Florida. I'd sell it to a friend, I'd buy it myself for a collectible. This is definitely the one if you're looking for a ivory white tricode Hellcat and to see more pictures of this car or one of other 550 new and used cars, trucks, SCVs, minivans, Wranglers, sports cars, challengers, chargers, Mustangs, Corvettes, Camaros, GT500, ZL1, Z06s, you name it we got to go to the website right there summitauto.com full pictures and descriptions of every single vehicle all at summitauto.com. If you want to check out more HD videos you can go to youtube.com slash summitauto click the bell notifications get updates in the videos I do each and every day and stay current on our ever-changing and vast sports car inventory here at Summit Auto don't miss out on a gem like this one by click the bell notifications and you'll get updated every time I do these videos in fact in a second we'll see link to subscribe to my YouTube channel the upper left a link to all the challenger videos I've ever done in the upper right link to this vehicle on our website in the lower left and a link to one of our latest YouTube videos in the lower right click those check us out we're super excited to help you with this ultra clean 2015 Dodge Challenger Hellcat and white ivory tricode metallic thank you so much for checking out the video remember to like subscribe and share on the YouTube channel I really appreciate it thanks again