Computing the System Frequency Response from Difference Equation

In the previous video, we introduced the Frequency Response H(omega) as an important system quantity that describes how the amplitude and phase of each frequency component of a signal are changed. As we continue to review related concepts, this video examines how to compute the Frequency Response H(Omega) of a discrete-time system when given the time-domain difference equation of the system. Our strategy in this case is to take the Z-transform of the difference equation to find the system transfer function H(z). Then, we evaluate the transfer function on the unit circle by letting z = exp(j*Omega). This yields the desired frequency response H(Omega).

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[cyrus]

I cannot thank you enough for your awesome and step by step explanation

[KarlLew]

Wow. I was surprised to learn that the magnitude of a complex fraction is the fraction of the magnitudes. That gem slipped by me long ago. Thanks!

[bepositive]

Thank you Adam. You are better than my professor :)

[shan]

Thank you sir! Very clear explanation and well constructed!

[michaelcoletti]

Thank you very much, very clear and HQ video!

[orangecat]

Hi Adam! Thanks for the great content! A quick question, when we write down the phase response in terms of tan^-1, does the range limit of tan^-1 also applies (i.e. tan^-1 returns a value between -pi/2 to pi/2)? If that applies, phase response 0 and pi will be the same (since tan(0)=tan(pi) periodic with pi), which contradicts the intuition that they are Not the same. Could you elaborate on that a bit? Great thanks!!!!

[crion]

what would happen if you have a z^-2 or higher?
if im right it's just e^-j2omega

[arrafzaman]

I have exam tomorrow and i blv my teacher copied your lecture, thanks sir