I was dying and dreaming of release. So zero points for creativity.   It's that time of year. Time for me to rant and rave. Today we're doing the ranting. Worst books of 2021 according to me. And these are worst books of 2021 that I read in 2021, not necessarily that they came out in 2021. I've done my best to actually rank them so they are in a particular order. That said, my number one is definitely my number one. And the least worst one is, I don't, yeah, I think that deserves to be least worst. But everything in the middle is, it could be moved around, but it's not hard and fast. Don't take those rankings too much to heart. But number one is for sure, number one. So anyway, let's do best of the worst to the worst of the worst. Once again, I do have to apologize if you can hear noise outside because they're doing landscaping outside, which I did not know would be happening today when I sat down to film. So thank you so much for that, I love that for me. So 10th worst, therefore the best of the worst is, I'm sorry, Alan, Shadow and Summer. I don't know if we're ever actually gonna have our chat about the books that he chose for me, but so here you go, Shadow and Summer, the first book in the long price quartet that I was very hopeful about, very excited to read. I plan to read it even if Alan had not chosen it for me because of Alan hyping it and him saying that it was to experience his tragedy. So I was hyped to read it. Now it's been several months since I read it and I never actually, part of it kind of helps to cement my kind of recollection of what I thought about a book is talking about it, explaining it, but I never did because I didn't talk about it in my wrap up because I was like, I'm gonna be talking about it with Alan and then I never talked about it with Alan. I've been trying very hard to keep it in my mind for the day that Alan finally decides to talk to me about it, which will never come. So here we are, so Shadow and Summer. Okay, so basically I just thought it was not very well written. I feel like the characters were, it's a lot of the complaints that I have very frequently, the characters felt wooden, they felt like plot devices rather than real people. The plot itself, it's spoilery so I won't say, but there was some, the thing that it ends up being sort of behind everything and how that all shakes out, when it was revealed sort of like, there's multiple things going on, right? And you're started following different perspectives and kind of trying to figure out who's behind what and whose agenda is this and what exactly they're trying to accomplish. So when you finally get to the end and you kind of finally see what was the thing going on all along and who was behind it and how they were going about trying to get that done, when it was revealed, I was like, I'm sorry, your plan was what? Like it happened to work out the way that you wanted it to because the author decided that it would and that's what makes a good plan, but I'm sorry that is the dumbest plan I've ever heard and there's absolutely no reason that you should have thought that that would actually work out. Like it's the type of plan where like that might work, but there is no guarantee.  So I was already annoyed with the writing style by the time I got there. And then when I got there, I was like, are you for serious? That was your plan. But then also there's just like a lot of weird choices the author makes where the opportunities to actually delve into what a character is thinking and feeling are just not gone into. And okay, so it's one of the most bizarre versions of telling over showing that I've ever seen, but so in theory, in a perfect world, you show what your characters do and there is gonna be some telling of course.  So there's some telling of like, they feel a certain way about something. But for them as much as possible in a, it's ideal to show them behaving in a way that makes you think they feel this way, if that makes sense, as opposed to just saying they feel this way. So instead of saying they are angry, I mean, sometimes for efficiency or if it's not that important, you can just say that. But ideally you get the sense for how angry they are, what type of anger it is, what they are angry about and how angry they are based on what you see them do, what you hear them say. And again, part of that is colored by speech tags that are like, he said angrily. But so in this world of this book, there are these elaborate hand signals that are sort of like the culture of this world that are invented by the author where you kind of do all this posturing and these physical ways of showing what you are thinking and feeling or to indicate like, to like ornament your speech, I guess, or to indicate to somebody how you've meant it. And so like, I already hate when books are, someone will say something sarcastically and then the author will be like, they said sarcastically and they're like, okay, I get it that that was sarcasm. I'm so glad you thought that I couldn't pick up on that. But here, almost everything, all this dialogue that there is, accompanied by he said in a posture that indicates that he means it both referentially but a little bit sarcastically. And they're like, so there's actually no nuance and subtlety to the speech, to the dialogue you've written. It's actually very wooden and plain and boring dialogue. But you think you've solved that problem by instead telling us what an elaborate amount of nuance is going on in the ways that they are posing. And I was like, okay, well, for one, like that sounds hilarious to me, just imagining the ways these people are contorting themselves. Because nowhere is it described what a pose like that is supposed to look like. So for there to be that many different poses that can be that many different things, they've gotta be like moving around like nobody's business. And then again, like it takes away all subtlety because part of what makes dialogue interesting to follow is you sort of following how somebody might be saying one thing and meaning another. But then if you were like, here's the dialogue that they said, but they said it in a posture that indicated they didn't really mean what they just said.  And then no, it's literally all the time. And sometimes they didn't even say anything. Sometimes they just like took a pose and that is their response. And the pose is again, leaving you in no doubt as to what they are thinking and feeling because there is a very specific pose to convey that particular combination of feelings. So I hated it.  And then I think there's a way to incorporate something like that where that's a unique feature of real building, right? To have a culture that uses more of a physical element, of a codified physical element to convey either information or feeling. But for example, in the wise man's fear by Patrick Rothfuss, there is a culture that does this. And it is not, it does not come across the way that it doesn't shadow in summer. There is a culture that shows no expression like on their face.  But then you come to learn that they have hand signals for how they feel about something. So this, again, the book isn't just like nonstop, you pose in a way to indicate that, it's an interesting feature of their culture and how that works. And there's still nuance to it and it's not constantly cheating by like instead of actually showing you the character you're thinking and feeling, it just tells you instead with a pose and a hand signal. So I think, I don't think it's impossible to do something like that. That could actually be quite interesting.  So it's the worst of the best because I feel like, like there was an attempt. Like that's, that could be a cool thing. And he definitely committed. Like we did not forget about, there wasn't a piece of world building that was introduced in the beginning and then kind of abandoned halfway through. We committed to the posing thing throughout. So I just, I feel like, I feel like it's like a recipe that went wrong.  So again, there was an attempt. Number nine on my list is Vesperteen by Margaret Rodgerson which was just the most methane that I have read in a long time. Probably since Sorcery of Thorns. The last Margaret Rodgerson book that I read. I really liked Enchanted Ravens and ever since then it's just been not that. So I guess Enchanted Ravens was a fluke, a one-off but Vesperteen was like literally everything that I've ever hated about YA except there wasn't really like an angsty romance so much. So like not that, but everything else. Like really shoddy world building, really painfully obvious things going on. A character that is an inch deep, a story that is kind of non-existent. It's kind of like just stuff happening and a main character that you're just like supposed to root for because reasons I guess. This book promised to be, I mean, if you don't know what it is, it's this young woman who's like, I guess a nun is the vibe, but so they're basically dealing with like the spirits of the dead and that's kind of her job.  It was so cringy and the moments that were supposed to be the sort of like deeper, more poignant moments about feelings of inadequacy or depression or whatever. They were handled so ham-fistedly, so obviously, so boringly, so without nuance. Have you seen it done so much better, so many other times? It's not like books haven't done this before. If this was the very first book to tackle these topics, I'd be like, you didn't do it good, but you did it first, so good on you. But so many books have tackled these topics with so much more care and while still telling an interesting story. And this just was not, and it felt like it wanted credit for credit's sake, just like it wants you to root for the main character because it's the main character. None of it was interesting or sympathetic or engrossing or atmospheric. For a book about, you know, spirits of the dead, it was zero spook, zero vibe, zero mystery, zero suspense, zero darkness. It was the most flaccid thing that I have read. Oh my God, I hated it so much. Next up, I have Deal With The Devil by Kit Rooka. This was a Plays and Bodice Rippers book club pick, which I kinda suspected I wouldn't love when I picked it up because it's an urban fantasy, or paranoid urban fantasy romance. And I don't really like urban fantasy or romance. I can like those things, I suppose, although I can't think of any urban fantasies that I liked. It's usually like in spite of it being that or because it does something to kind of transcend that or does something more than that. And romances, again, like I don't seek out for their own sake. I can like a romance that like by itself because it did a thing I really liked because it had really good characters. It had a good story. But like as a genre, it's not something that I just derive satisfaction from generally. So I suspect that wouldn't be a favorite. And then it was just, it was similar to Vesperteen and that like this is supposed to be, it's like the first in the Mercenary Librarian series. There is no library to speak of and it isn't a very exciting or adventurous plot. The love story in it was exactly as like sort of insta and ridiculous and unbelievable as I feared. And it didn't, I guess I hoped that if it's the Mercenary Librarian series that okay, it's an urban fantasy, okay, it's romance, but it'll have a cool atmosphere, a cool vibe, cool setting and I'll at least be on for that ride. But there wasn't one. And the part of it that was like, because it was pitched to sort of like being like orphan black, the one part of it that is where I believe that comes from is almost nothing like orphan black and it was both dumb and predictable. So I was just irritated with the entire time. And yeah, I knew it. Next up I have a book that I have a very lengthy video on so I'll link that down below, Half Sick of Shadows by Laura Sebastian. Laura, I forgot now. A lot of these books have gotten rid of. This purports to be an Arthurian retelling but from the perspective of the Lady of Shalott. And it was already a limp and bad story. Like it wasn't a new and grossing one. It wasn't an interesting one. The strange handling of timelines where it's telling it both in the past, the present and the future because she can see the future but she also has memories. So it's kind of like going back and forth between what she foresees, what's currently going on and what she remembers which removed all suspense and the lack of attention to any kind of cohesive historical detail. Like it wasn't even that she'd said it in a different time from Arthur's time but was like cohesively within this other time period. It was just a wibbly wobbly mess of just old timey time things that are from no particular era, no particular. Like it's, I mean, I attacked it for the fact that Arthur's story, unless you specifically said it in a different time, by default it takes place in the fifth and sixth centuries. But yeah, no. It was neither taking place in the fifth and sixth centuries nor was it specifically taking place in any other time period because the stuff that people were wearing, using, saying, having access to the modernity of their social norms and customs and practices. Just all of it was just such a mess.   So the person has a cohesive sense of what type of world we're in. What types of things are acceptable and not acceptable. What is the, like even if you're not going into detail about how governance operates, how the economy operates, how it's a taxation and property ownership, even if you don't go into those things, you're still gonna have a general sense kind of of how all of this works. And therefore a sense of what is possible for the characters, what is looked down upon if the characters do it, what is encouraged for characters to do it, like what world they are operating in. And if you have no clear sense of how patriarchal this is or how communist this is or how agrarian this is, if you have no sense of that, then all of it is just kind of like a mess that you have no sense of stakes or world or place for. So with Arthur in particular, that takes place in a specific time unless you say it doesn't. And this, like in addition to being wrong for Arthur was just also like on its own, if you forget when Arthur's supposed to take place, okay, forget fifth and sixth centuries, just take it on its own merits. Does this cohesively make sense within itself? It doesn't. It's all over the place.  It was just, I don't understand how people can even just like do some minimal Googling for this, but anyway, do not recommend. Next up I have The Last Final Girl by Stephen Graham Jones and other Blades and Bodice Rippers book club take. And this book is written kind of like a screenplay, but not actually a screenplay. Like it's not written like a script, but it is written kind of like, maybe like a storyboard for a movie where it's saying this character says this thing and then the camera pans over and you see the thing they are looking at.  And then we do a montage. And like that's how it talks the whole time.   But we committed. And then so in addition to just like, I don't think being a very good way to tell a story, the entire thing was utterly composed of references to slasher films, which I'm not intensely familiar with. I have seen a couple of slashers and I'm generally familiar with the tropes of the genre, like on a pretty surface level familiar with kind of what a slasher like the kind of beats that one has. And but these, this book is entirely composed of specific references to specific slashers. The dialogue is entire almost verbatim quotations from these things, the things that people are doing are again, references or homages to all of these other slasher films. And if you already find the story structure jarring because of the format of it, and then you don't get any of these references, like this book is literally designed to be only comprehensible to a select few people of the people who are this familiar with all of these slashers and who don't mind the format of this. Like you have, that is a small then diagram. And I am not even in either of these circles. So it's a real quick note for me. Next up I have Destiny's Captive by Beverly Jenkins. This is one of the books that Bethany made me read for our TBR swap and I did it. I've vlogged about it, so I'll leave that link down below. I'll leave the Blaine's and Potter Shippers show for our last final girl linked down below as well. Half of the vlog I did for the books that, the vlog I did for the books that she picked for me, at least half that vlog is just Destiny's Captive because again it's a romance, it's a Potter Shipper so you're not gonna be an automatic fave for me in the first place. And then everything about it. I just hated it more and more intensely as it went on. From the jump, the way this couple gets together is he black mails her into marrying him, which I'm like, well, that's a deal breaker and we have just begun. And then just from there out, the hypocrisy, the selfishness, the bizarre choices, with like completely unsympathetic behavior of particularly the male main character. The female main character is no great shakes, but the male main character, the love interest is, who is fantasy is this? Is what I wanted to know the entire time. I was just like the point of a romance. It's not even that like, you know, there is a questionable romance in a book but the book has other things going for it. But in a romance book, the thing you are there for is the romance, is the love story. And if the romantic hero that you are here to escape into a fantasy of being with is so just reprehensibly, off-puttingly unpardonable, well, that's the whole book. There isn't anything else to it, it's just romance books. So yeah, no. Next up I have Shadow of Night by Deborah Harkness. This is the second book in the All Souls trilogy, which is, it begins with the discovery of witches. I think when I did worst books halfway through the year, I might have put this Destiny's captive as worse than this and I might have swamped them now. Again, I said the middle bit is kind of, I'm not super married to these, to this order. But in any event, Shadow of Night took what was a lukewarm but somewhat promising beginning to a series in discovery of witches and just, so in the second book, we follow the same main characters, the witch and the vampire that we met in the present day in an Oxford in the first book. And they have now traveled back in time to the Elizabethan era, which was what I was excited for. I was like, well, the first book was okay, but I sure am excited to see them in the Elizabethan era and I should not have been excited for that because it was worse. The couple, their love story itself was much more insufferable in the second one than in the first one. It was already absurdly insta-lovy in the first book where you're like, you all just met, you know that, right? But they're like, I would die for you. And I'm like, a month ago, I didn't know who this person was. And then, so in this one, like that is turned up to, it was already turned up to 11 in the first book. It's like turned up to 21 now.  I would die for you. I can't live without you. I'm just like, oh, we got it. It loses all impact when it's constant. But then the weirdly, both intensely accurate and intensely inaccurate historicity of it where the author is, I believe a history professor. So she has like a great deal of knowledge when it comes to this. In the little things, in the clothing, in the food, in that kind of stuff, like lots of accuracy.  So that obviously, like there's a wealth of knowledge she's drawing from on that, but it is pointed out in the text how difficult it is for Diana to understand what they're saying, because back in the day, people talked way different. Even if you aren't in England where they speak English, they talked way different, not just the vocabulary, not just the words they're using, but their pronunciation of them all would have been wildly different. So it's pointed out that they find it difficult to understand Diana. Diana finds it impossible to understand them because she's, you know, a modern day American. And so that said, well, it goes out of its way to point that out, which like kudos, because that's how it would be. You can't just travel back in time and then just talk like normal because people didn't talk like that. All the dialogue between the old and day characters is weirdly modern and weirdly anachronistic and casual. And I just, I was like, you can't point out that they talk different and then have them talk more modern than anybody, you know, in an Austin novel, even though this is the Elizabethan era. And so I just, I mean, maybe that's the problem. Like you cannot have a time travel story like this for that reason, because especially not if you're gonna actually point out how this actually should work, which I would have thought to myself anyway, like if everyone had just like immediately talked, just find out, I'd have been like, well, they probably wouldn't. But the book points out that they probably wouldn't and then just proceeds to have them talk fine anyway. And I was like, what? So yeah, I hated that a lot. It was all, it was just mostly, it was boring, but it was also all those other things. So no. Down to the top three, which yeah, I think these are pretty solid at the top three. So number three is From Blood and Ash by Jennifer L. Armentrout, another blades and blaster book club fake. This was the worst. It is, it purports to be a sort of more like epic fantasy, historical fantasy type of setting and story from an author who has predominantly only written like urban fantasy or paranormal romance that takes place in the modern day. So it is written exactly in this style of a paranormal urban fantasy romance, except we now have corsets and daggers. But the vibe, the dialogue, the way the characters behave, it is all straight out of something modern. And I was told that, well, that's where the author came from. And I'm like, cool story. She's writing something else now.  Like no, well, that's great. Go back to writing sci-fi then cause you clearly still want to write sci-fi. If you've decided to change that, you've decided to try your hand at something else with that comes some changing of what you've normally done, but apparently not. Not if you're Jennifer L. Armentrout.  But that was painful. And then the story itself like didn't make a lick of sense. The characterization was so absurdly overdone and over explained and the metaphors that she would use. I have a whole vlog for this as well. So I'll leave that link down below if you wanna hear. All my nitpicks and all my gripes and all my hatred for it. I ranted about it at length in that vlog. So that's available to you. But it was like pretty much everything I hate. And the love story was like, in addition to just being kind of like insta-lovy and just like not a thing that I'm interested in reading incredibly toxic, but painted as like feminist and liberating. And I was just like, I don't think so. So yeah, do not recommend. Number two is Macbeth by Joan Esbo, not William Shakespeare. As you may or may not be aware, I have been reading the Hogarth Shakespeare retellings of Shakespeare plays with my friend Heather. We've been having live chats about them.  Heather actually de-enaftered it. She just refused to read it because it's also really long, which is ridiculous because Macbeth, I mean, already Shakespeare plays are fairly short. Macbeth is one of the shortest. So Joan Esbo wrote a book like this long that is supposed to be a retelling of Macbeth that he named Macbeth. All the other Hogarth Shakespeare books, they have a different title. Like the Winter's Tale is the retelling of that is the gap of time. The Hamming the Shrew, the retelling of that is vinegar girl. The Merchant of Venice, the retelling of that is Charlotte is my name. But Macbeth, the retelling of that, I don't know, it's called Macbeth. So zero points for creativity. And he wrote it as a sort of like cop drama. And I just, sir, I don't think you've read or understood Macbeth because not only was the book itself on its own terms, one of the most disgusting and boring and too long and self-indulgent and nail-gazy just awful books ever. Just by itself, if you forget that it's a retelling, it's just not good. But then as a retelling of Macbeth, so drawing the parallels and seeing which things are meant to be either direct translations of or mirroring or paralleling some part of Macbeth, either it's plot or a particular characters or whatever it is, as recreations of something out of Macbeth, I was like, I don't think you understood Macbeth. And this is not only like just not good. It's also low key offensive at times to the point where I was like, are you trying to ruin Macbeth on purpose? It was, anyway, Heather and I ranted about it at length during the live for it. Cause it was shockingly bad, frankly. I was like, who let this person retell Macbeth? They are clearly not qualified. I don't think they know Macbeth or they've entirely misunderstood Macbeth. So I do recommend Macbeth, the play. But Macbeth by Joan Esbo is one of the most garbage things I've ever been forced to endure. And it is also unpardonably long. My number one worst book of the year is the same as was my number one worst book, Halfwich of the Year. And that is Dreams of the Dying Maniclessly So. Which is a self-published book, which as I said before when I talked about it, I don't normally, I try not to go out of my way to crap on self-published or indie published books because it feels like picking on the little guy. But this book costs $40 in hardcover because the author obviously putting a lot of time, attention and detail and money into the aesthetic of the book. So the art that is outside of the Bumina cover art, the maps in the book, the BC area, like there's a lot of like bells and whistles and that's what you're paying for. The thing you did not spend money on is an editor because this book, again, in addition to not being a good story, having wooden characters that behave as plot devices and as vehicles for the author to not only info them, because he does info them, but to just spew his own philosophies and worldviews, which again, in addition to being painful to endure because that's not how characters should behave, they're also very basic and very not deep or fascinating hot takes on like the life or philosophy. These are like some super basic things that a middle schooler might be arriving at as conclusions when they're first beginning to ask existential questions. So it's just, it's painfully juvenile in what it thinks is deep and it spends so much time on these deep themes that I'm like, that's, are you kidding me?   So that was just like nauseating to read. But also it is so poorly written insofar as it is grammatically incorrect or there are idioms that are used incorrectly. Like that is not what that idiom means. There are weird, like not anachronistic isn't the right word to use since this is a fantasy world, but I don't know if there is a word for that. But so in a fantasy world, because you have invented this world, it is not our own world. There are things that people say that are based on things that are in our own world. So for example, biblical references.  Either this is taking place in our real world or there is something equivalent in your world that is like basically the Bible. Because otherwise that doesn't make sense why your character's saying that. So that's not an anachronism. I don't know that there's a word, maybe they let me know if there's a word for that. But there wasn't a lot of that going on. So non-stop, even while I was like angry and irritated with the story itself, which I think was badly written, there was all these sentences that I was like, well that's grammatically incorrect or that's not what that idiom means, the way that you're using it or that came out of the Bible. Why are people talking about this? So just the entire time I was like, I don't think fixing all the things that are objectively wrong with it, i.e. this is not how that idiom should be used, this is grammatically incorrect.  I'm just not deep. I'm sorry, I'm sorry, but it's not deep. And it was so long, it was so long. Partly because of all the soap boxing this author does about his own deep philosophies. But in addition to that, the story, what story there is wraps up at around page 500. And then there are like 200 more pages of falling action where there isn't even a story to be had. It's just wallowing in this character's misery and philosophy and issues. And I wanted to die. Dreams of the dying. I was dying and dreaming of release. Worst book by far that I have read, certainly in 2021 and possibly ever. It was so painful to read. And then it cost $40. So if it was like 10 bucks for a paperback and that was just like the story in it, I'd have been like, well, this could have used an editor, but I guess you are on a budget. But clearly you had some money to burn. And instead of paying an editor, you paid some artists to make it real pretty. So it's an added layer of irritation on my part where I'm like, I can't even give you that pass because you have demonstrated that this was not a priority to you that you could have fixed this. You had the money to fix this. And you chose not to. Those are my worst books of 2021. Let me know in the comments down below your thoughts and feelings about my thoughts and feelings. If there's any books you expected to see on this list or that you're surprised to see on this list. I want everyone to let me know. I post videos on Saturdays. Other other times as well, definitely Saturdays. So like and subscribe to my Patreon if you feel so inclined and I'll see you when I see you. Bye.


Hey everybody, I'm Tossus with RF Elements and in today's episode of Inside Wireless we'll learn about waveguides. A waveguide is a type of transmission line like a coaxial cable. It allows electromagnetic energy to travel through it and transport from point A to point B. Essentially a waveguide is a hollow metallic tube that can have various shapes. The most common ones are circular, single ridge, double ridge, elliptical, or rectangular. Like coaxial cables, waveguides work as low pass filters. They don't let low frequency electromagnetic waves travel through below what's called the cutoff frequency. Above this frequency signal travels freely in what's known as the first transverse electric mode, commonly abbreviated as TE10 mode. In this mode of operation the electric fields are always perpendicular to the walls of the waveguide and energy can flow freely from one aperture to the other. The upper frequency at which a waveguide is practically usable is given by the cutoff frequency when the next higher order modes start to propagate. At this frequency the field inside the waveguide starts to behave in a complex way and energy transfer is no longer optimal. This is why waveguides are mainly used in the band between these two frequencies called single mode bandwidth. The frequency we want to use determines the size of the waveguide. The lower the frequency the larger the waveguide is. For example at 300 MHz the size of a rectangular waveguide is 58 by 29 cm, while at 18 GHz its size is 1 by 0.4 cm. Waveguide diameter of a symmetrical horn is 36 mm. Waveguides are particularly useful in high power applications or where very low loss is beneficial. Other transmission lines such as coaxial cables always suffer from higher losses than waveguides. Additionally, they are also immune to external noise and have high mechanical durability. Waveguides are used in a variety of applications such as communication systems, radar systems and of course microwave ovens. For more interesting topics from the RF world, don't forget to subscribe, give us a like or comment below. See you next time.


Good morning and warm welcome to the 7th lecture on the subject of digital signal processing and its applications. We will spend a few minutes in recalling what we did in the previous lectures. In the previous lectures, we were looking at what an LSI system is characterized by. So we noted that for a linear shift invariant system, it is adequate for us to know what is called the impulse response or the response of that LSI system to a special chosen input namely the unit impulse. Once we knew the output of an LSI system given a unit impulse input, we know everything about the system. In other words, we know what the output would be for any input. In fact, we proved last time that the output, the input and the impulse response are related by an operation called convolution. The convolution of the input sequence with the impulse response sequence results in the output sequence. Convolution is an operation in its own right. What I mean by that is independent of the fact that it is an important operation in the context of linear shift invariant systems. Convolution can be thought of as an operation between two sequences irrespective of where the two sequences come from. In fact, there are reasons why we may want to think of convolution in that manner. And let us take a couple of situations where we need to deal with convolution as an operation independent of the context of LSI system. In fact, let us take a situation where we have cascaded to LSI system. So let us consider a situation where we have an input X of n being applied to one LSI system. Let us call it S1 with impulse response H1n, the output of which goes to a second LSI system. Let us give it to the name, give it the name S2. And here the impulse response is H2n and this results in the output Yn. This is called a cascade interconnection, a cascade or a series connection of two LSI systems. Now it is obvious that if we use the symbol star to denote convolution, then Y of n is equal to first Xn convolved with H1n and the resultant convolved with H2n. Here we have two convolution operations following one another to relate the input to the output. And there are several questions that we can ask. One question is what would happen if I interchange the order of these systems? So if I were to interchange S2 with S1, would it yield something different? Right? The other question that we need to ask is can I replace this combination, this cascade combination by one single LSI system? Right? So let us put these two questions down. Question one, what would happen if I interchange S1 and S2? And question two, is there one system, let us call it S, which can replace S1 and S2 equivalently. Now we will answer the second question first. In fact, the answer of the second question would emerge from trying to find out whether I can change the location of the bracket. You see? What I mean by that is suppose it were to be true, that means I could replace S1 and S2 in cascade by a single system S perhaps with impulse response Hn. Obviously the output would be Xn convolved with Hn, is not it? And we need to find out this Hn. And what do we actually have Yn to be? Actually Yn is Xn convolved with H1n followed by a convolution with H2n. So my difficulty is the place where the bracket lies. We shall show now that this is equal to Xn convolved with H1n convolved with H2n. In other words, we can change the position of the bracket for convolution. Is that correct? We shall prove this. This is what we shall now prove. And this property is called the property of associativity. So now we are looking at convolution in its own right, associativity of convolution. So in general what we need to show is that Xn convolved with H1n and here we do not necessarily imply Xn, H1n or H2n to be inputs or impulse responses. They are any sequences really. Now let us take the left hand side. I shall indicate to you the modus operandi of the proof and I shall leave some steps of the proof to you to complete. Is that right? So modus operandi of the proof or the method, the process to be followed to prove this is as follows. Consider the left hand side. Now Xn convolved with H1n can of course be written as summation on all k Xk Hn minus H1n minus k. Now essentially this is a function of n. This is not the whole left hand side. I mean this is just a part of it. So I am just, let me, so we are processing the left hand side. That is what I mean by putting this double line here. This is not done. We have just written one part of the left hand side. Now we complete this. So we have Xn convolved with H1n, further convolved with H2n to be summation on k. Now you see here I need to bring in one more variable. So I would not write n now. This is k but here I need to introduce one more variable. Let us call it l. And we put a summation on l now from minus to plus infinity and H2n minus l. Is that correct? This is the expression. This is the complete left hand side. Any doubt so far? Yes? Now we write the right hand side. And the right hand side is of course Xn convolved with H1n convolved with H2. And this is very clearly summation k running from minus to plus infinity Xk. And I need to write, you know, I will use this to denote the sequence obtained by convolving H1 and H2. This sequence evaluated at n minus k. Is that right? Whatever that sequence be. Now when you evaluate that sequence at n minus k, we know how to write the expression for the n minus kth sample of that sequence. We need to use a summation to write that sample as well. The n minus kth sample of the convolution can be obtained as follows. So this is summation k running from minus to plus infinity Xk and then I need to put a bracket. And I need to have let us say an m. An m running from minus to plus infinity H1n and H2n minus k minus m. Isn't it? I am evaluating the convolution at n minus k. Is that right? So what I need to do is to now bring these two expressions together here. I have this expression for the right hand side and I have this expression for the left hand side here. And I need to compare them. Let us write them on the same page with RHS which is summation k running from minus to plus infinity summation m running from minus to plus infinity Xk H1m H2n minus k minus m. And now it is very clear to us how to prove the equivalence of these two expressions. You see what we really need to do is to make a substitution of variable here. If we replace the variable l minus k with the variable m, you know the summation of k is common to both. As far as the summation of l here is concerned for any fixed k, you know remember the summation is from all k equal to minus to plus infinity. That means the summation is on all integers k and all integers l in the left hand side. And all integers k and all integers m on the right hand side. Is that right? And Xk is the term common. Now if we replace m for l minus k, then it is very clear that m minus l, what we need to do is to replace l. So l is then m plus k. And of course now it is very easy to see that n minus l would then become n minus m minus k. But the only thing we need to justify is that the summations are also correct. And that is very easy to see. You see k is as it is. k runs independently from minus to plus infinity. The question is what happens to m? For any fixed k when l runs over all the integers, m also runs over all the integers. So m which is l minus k here runs over all the integers when l runs over all the integers or vice versa. You see for a fixed k, l and m would concurrently run over all the integers. Of course not the same integer. But they would run over all the integers independently. And therefore one can replace this summation, double summation on k and l over all the integers by the double summation on k and m also over all the integers. And therefore the left hand and the right hand sides are equal. And that proves the property of associativity of convolution. Now we need to spend a minute in ensuring that we have no doubts about this proof. Do we have any doubt about the proof? Because it is a very important conclusion that we have drawn. So we have concluded that convolution is associative and that answers our first question. Convolution is associative. This is a more general conclusion we have drawn. And of course its implication for the context of LSI systems is that S indeed exists. The equivalent system exists. And that equivalent system has the impulse response h1 convolved with h2. Very interesting. Now we need to answer the second question. The second question is can I interchange the order? And that amounts to asking. You see now in a way we have also got an interpretation. We know that together the impulse response of the equivalent system is h1 convolved with h2. And if you could interchange the order then the impulse response would be h2 convolved with h1. So in other words we are asking whether convolution is commutative. In other words would h1 convolved with h2 be equal to h2 convolved with h1. Now please note that here I am abusing notation a little bit by suppressing the dependence on the integer index. I am just writing. And anyway you know in a way it is not too much of an abuse because ultimately convolution is an operation between sequences not between numbers. Is not it? It is not too much of an abuse of notation. So let us answer this question. Once again let us look at the left hand side first. So left hand side is essentially summation k running from minus to plus infinity h1 k h2 n minus k. And here again we make a very simple substitution. We substitute n minus k by l. And we note that k running from minus to plus infinity leads to l running from minus to plus infinity for fixed n. This is easy to see. For a fixed n if k runs over all the integers then n minus k which is l also runs over all the integers. And therefore we can make a replacement here. We can replace n minus k by l and that is very easily what we want on the right hand side.  And therefore we have concluded that the left hand and the right hand sides are equal and convolution is commutative. Yes, there is a question. Yes. Yes. So I will repeat the question. The question is you see we said that in this case for example when k runs from minus to plus infinity n minus k would invert so to speak. Or in other words it would seem to run from plus infinity to minus infinity. Well that is correct. I mean what I am trying to say is the set of integer the entire set of integers is covered by k and it is also covered by l. Though not necessarily in correspondence that means when k is at a particular integer l is not the same integer that is true. But there is a 1 to 1 correspondence. So for every k there is a unique l for every l there is a unique k and not only that the entire set is spanned. You know when you are dealing with infinite sets you have to be careful. So in fact the question has raised an important point. When you are dealing with infinite sets one must be sure that the infinite sets are equivalent. And in infinite sets you cannot simply you know conclude they are the same unless you can draw a correspondence. That means you must be able to if you claim that two infinite sets are the same are equal then you must be able to draw a 1 to 1 correspondence between those two sets. I must be able to make handshakes between the elements of the two sets and here you can do that. You can make a handshake between elements of the set k and elements of the set l a 1 to 1 handshake. So of course the handshake is not between the same elements but between different elements. Is that clear? Is that clear? Are there any other questions about this proof? So it is a you see we must it is very important that we clarify questions as we go along otherwise it would lead to gaps in understanding and weaknesses in foundation as we proceed. And a weak foundation leads to cracks on the upper stores upper storey the upper floors. Is that right? So foundations must be strong and then that does not allow cracks to seep in on the upper floors of a building. So are there any other questions on the proof so far? Yes is the proof very clear to everybody? So what is our conclusion? The conclusion is that convolution is commutative and in particular what does it mean for LSI systems? The order of a pair of LSI systems in cascade can be interchanged that answers question 1. Now I leave it to you as an exercise to prove the following that we have whenever we have multiple LSI systems in cascade let us say n capital n such systems in cascade any interchange any reordering is permissible. In other words the order does not matter if you have a set of LSI systems in cascade not just two of them any number of them then any reordering of those LSI systems in cascade does not influence the overall input output relationship. And to prove this you shall require both commutativity and associativity of convolution. Is that right? So please use commutativity and associativity to prove this by mathematical induction or any other method that you chose. Is that right? So I leave this to you as an exercise.


I've lived out of home and supported myself since the end of high school. I had no option but to juggle 25 hours of work and full-time study. It was hard. I was worried about my assignments, stressed about my finances and trying to navigate uni. On receiving the scholarship I was overwhelmed with joy. I stopped tossing and turning at night. I halved my work hours, had more time to study and my grades improved. This has led to me securing a paid placement in Shanghai later this year. 22 years ago I could never have imagined being where I am today. I can't believe it. This scholarship has changed my life and has fast-forwarded my career. I'm so grateful. When I graduate I'd like to help people in the human rights and the cybersecurity sector.


Imagine that you are a Eurypterid, a sea scorpion, one of the prehistoric beasties on the screen here. You're feeling pretty pleased with yourself. And why wouldn't you? With your terrible claws, compound eyes, and body sizes ranging up to two and a half meters in length, you made for a deadly predator, ruling the world's waters over 240 million years ago. In the present day, you are the subject of considerable scientific interest. Paleontologists studying the history of life learn how you're among the first creatures to walk on land, how you may have propelled an evolutionary arms race shaping the body plan from which all modern vertebrates, including humans, are based, and from a wider perspective, studying the demise of the Eurypterids and so many of their peers at the end of the Permian period, helped scientists build a chilling picture of what can happen in a world where greenhouse gases are allowed to rise unchecked. Something of great relevance today. Oh, Eurypterids, what the future can learn from you? Imagine your indignation then when you realize the tales you have to tell are not being heard. In the New York Times, for example, that bastion of journalism, Eurypterids have only peered three times in the last 30 years. The same goes for so many other prehistoric species with interesting and relevant stories to tell. Of course, you know who's to blame. It's those fatuous dinosaurs. Despite being of little scientific relevance and no more cool than you, they have appeared hundreds of times in the paper over the same period. They even appear in dozens of stories that have absolutely nothing to do with them. This is science journalism's dyno mania, an unparalleled fascination with a single topic which has the potential to displace other science from the news. Now, you'd think that such a singular and problematic phenomenon would have attracted the attention of science communication researchers, and yet it goes largely overlooked. Why? Because over two-thirds of science communication studies focus on the communication of just three disciplines, medicine, human biology, and climate science. Almost everything else gets generalized. And this is where my research comes in. Using paleontology as an example, my thesis aims to highlight the importance of acknowledging and appreciating these discipline level quirks in the way that science is reported. I am using an inductive, mixed methods approach with both news text analyses and interviews with media and science professionals. I've already identified some issues of interest. Of course, there's dyno mania, but we also see a similar bias towards stories on early hominins, one which oddly has not been challenged in the same way by the scientific community. Story selection seems to be based on an atypical set of news values, rating, for example, superlative-ness and references to elite fossils over more conventional selection criteria, such as proximity or numerical threshold. At the same time, the increasingly simplified framing of paleontological stories resonates with broader theories on the popularization of news, but causing to question recent assertions that science journalism has entered a new age of critical and engaged reporting. Public engagement with science is on the decline at a time when we need it more than ever. I believe passionately in improving the communication of science, and I hope that my research will add to the wider picture we need to achieve this. For paleontologists and for the Eryctorids. Thank you. APPLAUSE


Come to the session, this is Professor Farhad in which we would look at reporting on an examination of control at a service organization. Simply put, we're gonna be looking at the SAC report. We're gonna look at SAC report one. So we don't lose track of what we are doing. This is within the attestation and engagement that we can provide three levels of service, examination, review and agree upon procedures. In the prior session, we looked at prospective financial information, pro forma financial information, compliance attestation and management discussion and analysis. In this session, we're gonna be focusing on examination of the service organization control. And simply put, we can only have examination. So under examination is a yes, we don't provide a review. We don't provide an agreed upon procedures. Now for most of you, this concept, the control at a service organization is a new concept. Therefore, I'm gonna be defining terms before I start to explain the concept because it's very important that you define the players that are in this session. Starting with Farhat lectures. Let's assume my company, I have 10 employees, I don't, but let's assume that's the case. Well, here's what's gonna happen. When you have employees, you have to pay them. You have to pay salary. Well, that's easy. You just have to pay. But the difficulty in that is you have to withheld the appropriate amount of federal, state, local. If they have benefit, if they have health insurance, you have to withhold the appropriate amount, send the money to the insurance company. If they participate in a 401K plan, you have to withhold the money. If there's any type of withholding, then you are responsible for all of that. So you need the whole system for payroll. And what companies learned over the years, and you might notice this from your paycheck, that they outsourced this process.  Now those are not the only two companies, payroll companies. There are many other payroll companies that provide services for clients. For example, where I used to work, my CPA firm, my old CPA firm, Bucknall City & Company, we had a payroll company. One of the partners created a payroll company to compete with ADP and paycheck and simply put, in other words, to service our customers if they want the service payroll. So simply put, let's go back to my company. And my company, Farhat Lectures, has 10 employees. And as a result, I need to have a payroll system. Well, I don't want to worry about all the deductions. So I'm going to hire ADP. ADP is a payroll processing company. I'm gonna go ahead and hire them. And by the way, my cousin worked there, so that's why I chose ADP. So the first thing, we need to define few terms. Farhat Lecture is called a user entity in this context. The user entity is the entity that uses the service of the service organization. Now, who's the service organization? ADP is the service organization or the service provider. ADP is the service organization. It's the organization that provides services to user entities. Who are user entities? I am the user entity in this example that are relevant to those entities internal control over financial reporting. Now think of it this way. Now, Farhat Lectures, we have a revenue cycle or a revenue module. We have an expense module. We would have an operation module. And notice the payroll is a different one. Payroll is from an outsider. So basically what's embedded in my accounting information system is a foreign entity, a foreign system. Now, bear in mind that ADP is embedded in many different companies. And on a yearly basis, I have to audit my financial statements because my bank want me to audit the financial statement. So I'm gonna hire Adam CPA services to audit Farhat Lectures. Well, in order to audit Farhat Lectures, you need to learn about the internal control whether you wanna rely on them or not so on and so forth. Now, ADP is not part of my company. How is Adam CPA services going to audit my company, audit my payroll system if my payroll system is handled by ADP? Well, ADP knows this. So ADP also, they have an auditor or let's assume PWC and what they do, they are going to ask their auditor to do what? To report on the internal control over their financial reporting, specifically for Farhat Lectures over their payroll. So simply put, they will ask their auditor to issue a report to give some sort of an assurance for, in quote, Adam services or the other auditor. So simply put, Adam CPA services is the auditor of the user entity. So I hire Adam on a yearly basis to do my audit. Now, ADP knows about this. They know that I get an audit every year. They know that their client gets an audit every year. So what do they do? They have their own auditor. And for the sake of this example, they have PWC. I really don't know. I should have looked whether PWC audit them or not. But for the sake of the example, it doesn't really matter. Now, the service auditor will issue a report, audit reports to the auditor of the user organization. So PWC will issue a report to Adam company of the user organization about the internal control at ADP, specifically about the internal control over their financial reporting. And specifically for Adam, Adam is interested in the payroll process. The purpose of this is to build trust and confidence and the services performed. So now Adam CPA services, which is the auditor of far-hat lectures of the user entity will have some assurance, whether they want to accept this assurance or do their own testing, that's fine. But at least they have some assurance from PWC because PWC, they would issue a SOC1 report. And a SOC1 report will have two type. We're gonna have type one and type two. So notice it's SOC1, but it has two types. I'm gonna one and two, type one and type two. Before we proceed any further, I have a public announcement about my company, farhatlectures.com. Farhat accounting lectures is a supplemental educational tool that's gonna help you with your CPA exam preparation as well as your accounting courses. My CPA material is aligned with your CPA review course such as Becker, Roger, Wiley, Gleam, Miles. My accounting courses are aligned with your accounting courses broken down by chapter and topics. My resources consist of lectures, multiple choice questions, true-false questions, as well as exercises. Go ahead, start your free trial today, no obligation, no credit card required. So what is SOC1 report? SOC1 report is reports on controls at the service organization relevant to the user's entity, internal control over financial reporting, in case of Adam, specifically payroll. Now bear in mind, we also have SOC2. We're not gonna cover SOC2, but here's what I'm gonna tell you. SOC2 is very similar to SOC1 in contests and they have two types. Also SOC2, they have type one and let me write one properly, type one, SOC2 will have type one and they will have type two. They would also have two types, type one and type two. But SOC2 report on controls at service organization relevant to, notice security, availability, processing integrity, confidentiality and privacy. Simply put SOC2 deals with IT concern, whether you are hosting your data or your server at a third location, at a second location. Well, in other words, you're outsourcing these services rather than outsourcing part of your accounting system, which is ADP. Everything we're gonna learn for SOC1 applies to SOC2, except we are dealing with a different subject matter. Now then we also have SOC3, which is we don't worry about this, but basically it's a trust service report for service organization. SOC3 report is for general distribution. Obviously what I'm implying, SOC1 and SOC2 are of limited distribution. So now we need to talk about SOC1 reports. A little bit more. Remember we have type one and type two. Again, what is SOC1? It's report on controls at the service organization that's relevant to the users, entities, internal control over financial reporting. What is the purpose of it? Again, this is a review. To meet the needs of entities that uses the service organization. Well, to meet the needs of far hat lectures, I have clients, I have customers, I have an auditor. They want to have some assurance about my payroll. Well, guess what? The SOC1 report will give them that assurance. Remember Adam company that audit me is responsible for understanding my internal control. How are they gonna audit ADP? Well, PWC will give them some help. There are two types of report on control that PWC can provide. This is gonna be type one report. What is type one and what is type two?  I would say it's easy to remember, but let me go through it step by step. Type one report on management description of a service organization system and the suitability of the design of the control. So simply put, they'll give you a report explaining the internal control, narrating the internal control, the description and the design of it. Also, they'll give you some written assertions about the control and they provide you an opinion. So this is what a type one is. Simply put, this is how the control works. They may give you flow charts. They can show you the design of it, but that's about it. This is type one report. Type two report on management description. Hold on a second. Didn't type one report on this? Yes, type two would report on this and the suitability of the design. Hold on a second. We just said this. Yes. So type two is simply put type one plus the operating effectiveness of the control. Here, when they give you a type two, it means they tested the control and they are giving you a report about its effectiveness. So you really want type two. If you're Adam Company, you want more assurance. Well, they can tell me what the design looks like. They can describe it to me. They can show it to me. But hold on a second. If they're gonna test it and tell me how well, if it's operating effectively or not, I would like that. So type two would include type one plus a report about the operating effectiveness. More assurance. Obviously, it's gonna include written assertions about the control and not an onion. They will provide me an opinion which we'll talk about later. Let's focus now on type one report. Once again, type one is when we express an opinion which is an examination about the fairness of the description and the suitability of the design. That's all what we do in type one. So how would the service auditor, how would PWC come up with that conclusion, the service auditor responsibility? Well, they obtain and read the system description prepared by the organization and assess whether the description is fairly presented. Simply put, we're going back to audit 101 and learning about the internal control. We evaluate whether management use suitable criteria and preparing and presenting the description. PWC would evaluate whether the organization description include information about procedure by which description are initiated, transactions are initiated, authorized, recorded, processed, corrected, reported at the user's entity, so on and so forth. Simply put, they learn about the internal control as we do in a regular audit. They would also evaluate if the control has been designed to address risk threatening the achievement of the control objective. And what would they tell you in the report after they do all of this? Here's what they will tell you. If control working as described, basically they learn about it and they think it's a great control on paper, they would say if it's working at describe, it should provide reasonable assurance that you will be able to mitigate the risk. Okay, you would not be basically put, provide reasonable assurance that the risk would not prevent the achievement of control objective. But it's good, that's what we want. But all what they're saying, if it's working properly, that's all what type one is. And they give you the description and the suitability. Type two report would include, as I said earlier, type one, I know I'm repeating this several times, but this is what they test you on, what's in type two. Type two is type one engagement plus the service auditor PWC perform test of the operating effectiveness. And this is great, this is what you want to do. This is what Adam wants to see, type two report. Type two report contains three opinion. One, and I divide one into two, a description which we talked about in type one and suitability also on type one. And by the way, I did not mention this, I'm gonna mention it now. Type one report is a point in time. So it has a date, for example, December 31st, 20x4, a point in time. In addition to those two opinions about the description and suitability and we'll look at the opinion later, they give you the operating effectiveness. The operating effectiveness of the control is for a throughout a period, for a period of time. Okay, for example, for six months ending December 31st. It's a period of time rather than a point in time. You remember how the balance sheet versus the income statement, the balance sheet is a point in time, the income statement is a period of time. The operating effectiveness is throughout a period of time. Now, remember, you have to restrict both report, restrict the use of the report to specified party. Who are the potential specified party? Who do you think? Well, the entity itself, of course, its customers might want it, suppliers, business partners and regulators. So you don't distribute it to the general public, but if someone asks for it, they have a use for it, you understand it, here's the report, type one and type two. Now be aware that the user auditor should evaluate the competency and the dependence of the service auditor if you want to rely on type one and type two report. If you want to rely on their description or on the operating effectiveness, whatever PWC is saying, well, you wanna make sure they are competent and make sure they are independent. You should evaluate the relevant control at the user entity and obviously at the user entity. Of course you have to do that. And at the service organization to assess the risk of material misstatement, you might have to do some testing. Although you have type one and type two. Now type two is very helpful. If you really trust them, just don't have to do any testing.  And if that's what you wanna go with this, that's fine. Or you might have to collect some information yourself. Now you have to issue an opinion. You could have various opinion. You could have unmodified opinion. And an unmodified opinion, you don't refer to the service auditor. There's no division of work here. If you have an unmodified opinion, that's great. If you have a modified opinion, if you modified the opinion for any reason. Now, would you refer to the service auditor? Well, if referring to the service auditor help clarify or understand the modification, then you will do it. Otherwise you would not. If the service auditor has nothing to do with the modification, you don't have to worry about this. You could also give a scope limitation. What is scope limitation? You cannot obtain sufficient appropriate evidence about the services given by the service organization relevant to the user's entity financial statements. You cannot, you're not comfortable with the evidence.  Now let's discuss what a report for type one would look like. You have the word independent in the title would have an address C, the nature of the engagement plus the date, the service organization responsibilities, the service auditor's responsibilities. We followed the ICPA standard. They would describe the examination. They will disclaim the opinion on the operating effectiveness. Remember, we are dealing with a type one report. In a type one report, you don't test the operating effectiveness. So that's why I highlight this in yellow because when I show you type two, it's not gonna be there. So that's why I'm highlighting it in yellow. Then you will discuss the inherent limitation, basically no internal control is perfect. And you will give your opinion. Remember, type one report has two opinion. One about the description of the internal control and the suitability design. Two, then you restrict the distribution. So this is type one. Now type two would look mostly very similar except you're gonna have three opinions. This will not be there, right? Because you are going to test the internal control. Type two, the word independent address C, nature of the engagement date, service organization responsibilities, service auditor responsibilities. We followed the ICPA description of the examination and her and limitation opinion. The opinion will have description and control suitability design, which is the type one. I know I'm saying this in so many different time and so many different ways. That's what they test you on on the CPA exam. That's why I keep telling you this, this way, then the other way, then the other way, but it's the same information. Then the third one is control, control tested operated effectively. That's the third opinion that they tell you about. And they describe the test. How did they test the internal control? They use sampling, whatever they did, they will describe it and they would restrict the distribution as well. Now, what should you do? Go to FARHAT lectures and work MCQs. That's going to help you understand this important topic on the CPA exam. Recently, SAC report has been tested heavily and it's considered an important topic. Good luck, study hard, stay safe and the CPA exam is worth it.