The Mathematics of Signal Processing | The z-transform, discrete signals, and more

This video goes through an overview of what you would learn in a discrete time signals (or digital signal processing) course. Sampling, digital filters, the z-transform, and the applications of these are some of the things included. I had to over simplify a lot to barely keep this video under 30 minutes but hopefully it gives you an idea of how this type of math is used in the real world.

►My Setup:

[vojtechstrnad]

Don't be worried about making long videos. This video could be two hours long, and I would still watch it in one go.

[chuckkhubbard]

Man, I was searching and searching, and so many videos just want to give "an overview", and then the people just wax poetic for 15 minutes about the subject, with no details. Thank you for jumping right in!!
I hope to understand it better tomorrow after the alcohol wears off.

[Pupsi]

Audio rookie mistake 22:28. Using the filter wasn't the cause of distortion in your signal. What's actually causing your signal to distort is digital clipping that happens during the combination of your speech signal to that -0, 0Db 1KHz signal 19:49. The majority of frequencies below 1KHz should be almost unaffected but above 1KHz they are more or less reduced to a square wave. The amplitude of a digital signal caps off at -0, 0 Db beyond which no information can be stored and will result in distortion. Combining the two signals here would have required information to be stored above -0, 0 Db amplitude. Try reducing both signals by 10-20Db and then combining them. You can also hear what the filter actually does by applying it to the pure signal of your speech.

[sagarjaju]

Don't worry about the length. It's important that you keep the important points intact. And if the videos are longer than this, I would still watch.

[tammygoyal]

0:30 example
1:10 parabola, rational
4:10 moving average sample - cos
8:30 unit circle
10:00 vector z and y(z)
11:30 Manipulate algebra -average sample
12:50 algebra = pole and 0 to z
14:30 signals 0 average filtered out
15:30 fixing normalized frequencies
17:00 low pass filter - higher frequency filtered
17:45 frequency spectrum (what makes it up) spike = frequency,
19:00 audio
21:00 remove one tone
22:00 never ideal, removed original
23:00 using equation and notch filter
25:00 summary code poles change
26:30 filters change
27:00 applications

[nonojak]

How does this guy explains a whole semester-long course in a single video better than my professors did in 15 hours!?

[clcsqueejy]

As a radar engineer, this was a fun video to watch. Was really cool to see you tackle this topic, since it's pretty dang specialized, like you said.

[watcherofvideoswasteroftim]

I've watched this video multiple times at different points in my Signal Processing courses and every time I learn something new. Thank you Zach!

[johnyepthomi]

This channel is a boon to humanity. Keep doing what you're doing.

[gsp_admirador]

I wish I had professors like you at my college 😔

[AB-olfv]

This cleared the whole connection between z-transform and poles/zeros, and the link between circle and sinusoid. Much appreciated.

[ayushkumar-zrlp]

I am an electrical engineering graduate and I love this
In college we are taught the theory that makes things kind a boring but only thing that isn't boring is understanding the meaning of these things in reality
Thank you so much for such a video.

[nihargupte]

That's the best ever explanation about Z transform I can ever get. Thanks a lot man, really made my day.

[govamurali]

Finally, I understand why Z transform is used. Thanks!!!

[jaikumar]

Thanks a lot Majorprep !! I requested this in previous video and you promised this... this video intuitively explain digital signal domain specially Z- transform

[SKARTHIKSELVAN]

I took several days to understand Z transform. You finished it in 30 min. Thanks.

[drinductor]

Makes whole video about electrical engineering... uses i instead of j. smh

[karthikmg]

Thank you sir im an engineering student n was struggling to understand these concepts of lapace n z transform u gave a clear intution thank u so much

[arvindp]

Sharing information is the best way to preserve it. Thank you so much!

[mukuljobra]

It was really wonderful looking throughout the whole video, in every minute, you just simplified very in-depth topics, especially about what power the DSP is actually holding in the digital era. Make some more videos on similar stuffs like Laplace and Fourier transforms, the world must need to know what actually these two geniuses have given to us.
Great 👏🏻👏🏻👍🏻👍🏻