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Finding the System Frequency Response from Pole/Zero Plots

http://adampanagos.org The transfer function of a general discrete-time linear system is analyzed. In general, the transfer function is a ratio of system poles and zeros. When determining the frequency response of the system, we replace z in the transfer function with z = exp(j*Omega) to obtain the system frequency response. By representing the pole and zero locations in polar form, a “nice” representation of the frequency response can be found. We see that the Amplitude Response of the system at a certain frequency is just a ratio of distances between a point on the unit circle to system zeros/poles. Similarly, the Phase Response of the system at a certain frequency is just a summation of angles from a point on the unit circle to the systems poles/zeros. Knowledge of this representation allows one to design filters with desired Amplitude/Phase characteristics by placing poles/zeros in the complex plane. The next video in this playlist is: Matlab System Frequency Response from Pole/Zero Plots -    • Matlab System Frequency Response from...   The previous video in this playlist is: System Frequency Response Examples -    • System Frequency Response Examples   Join the channel for membership perks:    / @adampanagos   Course website: https://www.adampanagos.org/dt-signal... If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!