The convolution theorem and polynomial multiplication

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This revision fixes the following errors and suggestions that were found by my readers:

This update continues the journey of understanding transfer functions. It provides a brief understanding of the difference between the time domain and the frequency domain. I hint at the awesomeness that is the Fourier Transform (more to come on this!) and show how convolution in the time domain is really just multiplication in the frequency domain.

There is also a new side note in the convolution section - as was recommended by a reader - that shows how polynomial multiplication is really just discrete convolution of the polynomial coefficients. Pretty cool actually.

Thank you for all of your support and I hope this helps you on your quest to understand control theory on a more intuitive level. Cheers!
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At 1:44, finally this is the exact screen that helped me understand convolution after ~14 years. I didn't understand during uni... and I just decided today to figure it out. Thanks!

MattCookVideos
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Oh wow, I actually never thought of convolution as polynomial multiplication. This makes so much more sense now, even though it is a couple of years since I took my signals & systems exam. I bet you can extend that then to the Taylor series of continuous function quite easily. Neat!

DisdainforPlebs
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You are my hero. There has never lived so noble a systems engineer.

oogalook
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Thoroughly enjoying the book so far Brian. I look for forward to each update.

rgarry
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Another awesome sauce Brian. I never thought about multiplying polynomials this way. Can't wait to read it!

davidcanada
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It is an amazing book! I couldn't be more thankful!

sky_
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Thanks, I am always confused about fourier transform and searching for a good book.Hope this is going to clear all my doubts.

saimanojnelavelli
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I never knew that, Convolution sum originates from the response of a LTI system given the impulse response, its interesting to see it also gives us product of two polynomials, i wonder if there are any practical or mathematical implications of this.

tmfelwu
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Just a quick question. In your previous video about LTI, you mention the example of mass on a spring producing a frequency response as a sine wave when it is imparted with a impluse function, and here you mention it as cosine?

amulu
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Is it possible to donate and get the book without using paypal but mastercard debit card? If i choose to donate and choose "continue to next step", it directs me straight to paypal.

martinl
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Sir please put up a lecture tutorial on periodic control systems

ajitiist
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I just purchased your book. Do you have a pdf as opposed to the html. Thanks

DavidLeeMenefee
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Hi Brian! Thanks to you I'm entertaining the idea of doing a PhD in Control Theory. Can you recommend some Universities for me to apply to?

matthewjames
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Very nice! Is there any rough estimate of when the book will be complete (first version, at least)?

RSP
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Hi Brian, I'm really curious. Have you ever found yourself motivated to study the pure maths behind all the theories that you've encountered as a control engineer? Have you ever studied pure maths rigorously?

AlqGo
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How long is your book now? I wasn't sure if I should get it, but now I think I'll get it and print it out for the new students to use. It looks more readable than our current control theory textbook

CanadianRocketry
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I think my chrome browser was temporarily blocking those header download links because they weren't showing up. But after doing many refreshes they all of a sudden appeared. FYI...PEACE

DavidLeeMenefee