Answer Happy

6 Lab Exercise: Filter Design In this section, we will use Pez to place the poles and zeros of H(2) to make a filter with a desirable frequency response. Filter design is a process that selects the coefficients {ak} and {bk} to accomplish a (a) FIR Filter (b) Feedback Filter 2 6 5 1.5 I M w 0.5 1 -85 -0.25 0.25 0.5 -0.5 -0.25 0.25 0.5 0 D/2Tt 0 @/21 Figure 1: Magnitude response of two unknown filters. Frequency axis is normalized (ô/29). Use Pez to help you find the filter coefficients that will match these frequency responses as closely as possible. (a) Second-order FIR filter. (b) Second-order IIR filter. given task. The task here is to create a filter that has a very narrow “notch.” This filter would be useful for removing one frequency component while leaving others undisturbed. The notch filter can be synthesized from the cascade of two simpler filters shown in Fig. 1. (a) Start the process by using Pez to design each of the filters given in Fig. 1. (You will have to determine the locations of the poles and zeros from the plots in Fig. 1.) Both filters are second-order. Make sure that you enter the poles and zeros precisely. Pez will do the conversion between between root locations and polynomial coefficients, but you could also do this with the MATLAB commands roots and poly. You can check your results by also calculating the filter coefficients by hand (see the next section on polynomials with complex coefficients). Record the coefficients of your filters in the table provided Note: Use Pez or freqz () to verify that the frequency response of each filter is correct.

Zero 1 Zero 2 Pole 1 Pole 2 FIR filter (filter 1) TIR filter (filter 2) Cascade of 1&2