Z Transform Region of Convergence Explained 

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Thanks so much. I really appreciate hearing from people who are finding the videos useful - especially people like you, who have watched all of the videos! Very impressive. I'm so glad they have been helpful.

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That's great to hear. I'm glad you found the video helpful.

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It's animations "old school" 😁 Sometimes the old ways are the best. I hadn't realised I'd been doing it "casually" though. I probably wouldn't make it as a magician. 🤣

Thanks for the suggestion, I'll give it some thought.

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Glad it was helpful! If you haven't done it already, you might like to try some of the other videos on the channel too.

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You are very welcome. I'm glad you liked the explanation. It's how I would have liked to have been taught too! 😁

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Thanks for the suggestion. I'll add it to my "to do" list.

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Yes, you've got it, that's right.

Thanks for the suggestions. I've added the Hilbert transform to my "to do" list, and moved the low pass equivalent topic up the priority order.

Very well sir. Thank you once more.

The distance between the poles and the imaginary axis affect the spectrum response. See this video for more details: "How do Poles and Zeros affect the Laplace Transform and the Fourier Transform?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-iP4fckfDNK8.html

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Yes. The ROC of cos(wn)u[n] is |z|>1 (ie. not including the unit circle |z|=1).

No. It means that if you modify the impulse response, by multiplying it by the function 1/r^n (for r>2 in your example) then you can take the Fourier Transform (ie. then the infinite summation converges). Then you can perform calculations in the "z/Fourier domain", and if you need to, then you can also transform back into the (discrete) time domain. If you actually want to make your system stable, then you would need to change the design of your system (eg. electric circuit) so that it has an impulse response that is stable.

@@iain_explains Q#1. How is this information useful then? Since when we multiply impulse reponse by 1/r^n it will modify our orignal signal (impulse respone) and then its Fourier Transform would not tell information about the impulse reponse but of the modified signal. Q#2. Since we already know that our O/P is unstable, causal so what is the purpose of calculations in "z/Fourier domain"? Also tell the purpose of finding Z transform/ROC in this case?

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Thanks for your nice comment. Glad you liked the video.

@@iain_explains i want a lecture Fourier series ...please can you make on it

It's a generalisation of the frequency domain. See this video for more details: "What is the Z Transform?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-n6MI-nEZoL0.html

@@iain_explains thank you. :)

The basis functions (waveforms) for the Z transformation are z^(-n), where n is the time index. For example, when r=1, these basis functions are the waveforms cos(wn)+jsin(wn), which are time domain waveforms (remember, n, is the time index), at the frequency w. So, in general, the basis functions (waveforms) are r^(-n)(cos(wn)+jsin(wn)) which are "damped" versions of cos and sin (for r>1). So, "physically", w is the frequency, and r is the damping coefficient.

@@iain_explains Thank you very much. I will review your videos again, I really began to understand signals from this channel.

I'm glad you liked the video. Sorry, I'm not sure what you're referring to though. Where do I mention Z = ρVs ?

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Breaking Bad or James Bond?

@@iain_explains breaking bad , you look like bryan cranston .. thanks the video u helps me alot and i have an exam today thank u again sir👍🏻