5. Z Transform

[@necrowizzard]

'when I introduce something, I wanna think about how the thing I just said, relates to everything else I've ever said'

[@youmah25]

plato???

[@shrinidhi111]

The introduction to Z Transforms was simply brilliant.

[@wintermute701]

30:29 student turns into pigeon

[@djtoddles8750]

29:09 it's b/c he used emacs - he should have used vi of course. Seriously this guy is fantastic, great instructor and a sense of humor as well

[@ardasevinc4]

that intro (everything until the first ~10mins) is PHENOMENAL

[@mastodans]

I love to see active learning in science classes

[@cbbuntz]

Fibonacci sequence as an impulse response!

[@djtoddles8750]

26:38 There's a Y(x) term and X(x) term in the middle equation. Should that be Y(z) and X(z) or am I confused?

[@uriel_zapata]

he said that was a mistake.

[@djtoddles8750]

@@uriel_zapata yeah I realized that about two minutes later, lol. But thanks for mentioning, nice to know people are on the boards and of course that people are watching the vids themselves , which are amazing

[@rockspoon6528]

All your mistakes are never forgotten.

[@shrinidhi111]

17:06 "Theory Of Lectures". Lol ⛄

[@djtoddles8750]

It's very meta

[@aricgerspacher1071]

43:50 How is x(0) = 1? Is x(n) assumed to be a delta function?

[@noobieexplorer4697]

yes. we are trying to find unit sample response

[@abhimittal6885]

46:41 How the two expressions are added? Should n't there be a negative sign between them? (in terms of n, after the heading 'NOW'))

[@BENJAMINHAMANE]

this lecture is very impressive

[@ubermensch8022]

Damn, he sounds like Gavin Belson.

[@PedramNG]

Amazingly taught👏👌

[@EmreYavuzalp]

Is this for computer engineering?

[@ibrahimokmen6216]

Elektrik Elektronik Mühendisliği sinyaller ve sistemler dersi :)

[@djtoddles8750]

yes but DSP and z transforms specifically are useful in other branches of engineering too, and from what i've heard dsp will become more important as time goes on throughout science and engineering

[@joshmdmd]

28:43 I hate this person in all my classes.

[@MoutasemMohammad]

LOL

[@cunningshark]

that person is too cautious, maybe. and I hate that kind of "smart"

[@ian2668]

I think it's riskier to say "You are wrong prof."

[@UniverseGOD2525]

my exam is on day after tomorrow

[@HJohannes93]

Same here, at the time I'm writing this haha ;)

[@l.g3765]

same

[@HansNiemann762]

lol same here , but at this moment

[@suzankhan797]

Same Here 🤞

[@kronologie]

10:14

[@valtih1978]

I think this is one of the most appropriate lectures on z-transform. He tries to relate things rather than bore us with the regions of convergence. The only problem is that he gives too much time to the students to think. This is really boring. He could spend in more efficiently tying things more tightly.

[@alexandervolkov2661]

He introduced z-transform by way of using a delay operator, which has an "out of the blue" feel to it. The more appropriate way, imo, would be to introduce DTFT first, then, by way of, sort of, stepping out of the unit circle, using eigenfunctions, and connect the latter (DTFT) with the former (z-transform). As a boon, this way the ROC comes in naturally justified.

[@ishankulkarni3542]

why classroom is half empty.....

[@Rollmops94]

Watching this makes me sad. I recognize this style of teaching from my own education, but it's not good. In the real world people have a real problem they want to solve. So they invent tools. The z-transform is such a tool. To just define it out of the blue and then "explore" its properties leaves most people clueless about why and how it was designed, which would not only give a much deeper understanding, but also train the students capability to solve problems on their own.

[@chriszhang5781]

Could you explain what the real world problem was and how it caused the invention of z transform?

[@Rollmops94]

@@chriszhang5781 Not really. I don't know the exact problem, that lead to its creation, but I can make one up. A little warning heads up though: This is going to be long and I am going to explain a lot of stuff, as I can't expect you to have any special knowledge. There is the idea of a filter, which gets used in music for example. Many amplifiers have these little knobs to adjust the bass, mids and treble of sound. These are filters. A filter's functionality is rather simple to do in the analog/real world - the simplest being just a resistor and a capacitor in series - but rather difficult to do digitally (with pure information and math). This is comparable to the problem of finding the volume for a complicated body. You can do it the hard way mathematically or you can just measure the amount of water it displaces and let reality do these calculations for you. You want to do it the hard way, so here we go: To build a digital audio filter you first of all need to understand, what sound is. So let's go way back. I think many people don't realize, that we live in a giant ocean. The ocean is made up of air and even though it is very hard see, smell, taste, hear or feel and therefor very easy to forget, it still surrounds us - and just like fish - we die when we leave it for too long. And just like water makes waves whenever something moves through it - air does as well. A driving car creates ripples in the air. A running tiger does also. For humans it is especially important to perceive moving things, as moving things have the highest potential. They can potentially kill you - like the tiger and car - but they can also mean survival - like prey, a river or another friendly human. This is where your ears come into play. Your ears are shaped in a very specific way to guide the waves of the surrounding air into these little holes on both sides of your head. Inside these holes there is a thin membrane - like a plastic foil - which gets hit by these waves. This membrane is so thin, that it moves back and forth with every wave. Your ear can sense these movements and translates it into data, which is send to your brain for further processing. In your brain the 'height' of these waves is interpreted as loudness/volume and the 'length' of them as highness/pitch. The result of this complex process is what we know as hearing. Long story short: What we know as pitch or bass, mids and treble is ultimately the 'length' (scientifically called frequency) of a wave. So when we want to cut the bass, what we actually want to do is filter out the low frequency waves of a signal - hence we call it a filter. When we think about the fact that what we hear is an overlay of many, many different waves with different speeds and different heights and different timings - it becomes clear that it is rather difficult to find a specific set of waves in this chaos. It is comparable to you trying to figure out how exactly I mixed this color🔵from a large set of pigments. To the rescue comes a brilliant idea: Imagine you take a periodical signal (a signal that repeats) and revolve it around a circle at varying winding frequencies. There will be certain winding frequencies at which the revolved signal becomes asymmetric, as it aligns with itself. What that means is that the winding frequency at these points matches the frequency of the periodical signal. I actually took the time to make this little program to help understand this idea: jsfiddle.net/teachMeWebDesign/opqamzve/722/ The blue slider sets the winding frequency, while the orange slider sets the frequency of the sinus function. The points were the results looks the least impressive are the points where the winding frequency matches the sinus frequency. From here on the only question that's left is how the actual math, that realizes this idea works. You got quite refined formulae in z-transform, fourier and laplace, but it can be solved with high-school math just fine. Hope this actually helped and didn't confuse you even more.

[@chriszhang5781]

@@Rollmops94 OMG Thank you a lot for the long reply, I'll be sure to read it later

[@bmoreno-ri8]

Such an amazing answer@@Rollmops94 ! thanks for it :)

[@PankajSingh-dc2qp]

True.. This course doesn't seem to be signals and systems class

[@alingeorge8160]

amazing lecture thank u sir

[@gg9565]

This dude is just that ni**a, I swear

[@prabuddhbharat2934]

I knew almost all the answers but they didn't .. r they from MIT...😂