Demonstrating in the Classroom the Ideas of Frequency Response

One of the most persistently difficult concepts to communicate to students is that of “frequency response”, because it spans both the frequency-domain and the time-domain. This paper presents a Matlab-based graphical method of demonstrating several important relationships among pole/zero locations, Bode plot (i.e., Fourier transform), and time-domain sinusoidal response. The author has been using this method successfully for several years in a variety of systemsrelated courses to help students understand these relationships. The software is also easily available to students, so they may reconstruct classroom demonstrations, and do much more. In the demonstrations, Bode magnitude and phase plots are programmatically linked to plots of the pole/zero map and of the time-domain sinusoidal response. The frequency of the stimulus sinusoid can easily be changed in any one of the plots, with the change automatically propagated to all the other plots. All of the plots have interactive capability, and display much more information than simple line graphs. These plots are used to enhance discussion of (1) minima and maxima in the Bode magnitude plot and their relationship to pole/zero locations, (2) graphical (vector) analysis of the Fourier transform, (3) steady-state response versus transient response, (4) steady-state magnitude and phase and their relationship to the Bode plots, and (5) phase-lead and phaselag. Complete details of the method are presented. The software is available on the web, and is free if used only for educational purposes.