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### Example LPF Frequency Response Using freqz

Figure 7.2 lists a short matlab program illustrating usage of freqz in Octave (as found in the octave-forge package). The same code should also run in Matlab, provided the Signal Processing Toolbox is available. The lines of code not pertaining to plots are the following:

  [B,A] = ellip(4,1,20,0.5); % Design lowpass filter B(z)/A(z)
[H,w] = freqz(B,A);        % Compute frequency response H(w)

The filter example is a recursive fourth-order elliptic function lowpass filter cutting off at half the Nyquist limit ( '' in the fourth argument to ellip). The maximum passband ripple8.2is 1 dB (2nd argument), and the maximum stopband ripple is 20 dB (3rd arg). The sampled frequency response is returned in the H array, and the specific radian frequency samples corresponding to H are returned in the w (omega'') array. An immediate plot can be obtained in either Matlab or Octave by simply typing
  plot(w,abs(H));
plot(w,angle(H));

However, the example of Fig.7.2 uses more detailed compatibility'' functions listed in Appendix J. In particular, the freqplot utility is a simple compatibility wrapper for plot with label and title support (see §J.2 for Octave and Matlab version listings), and saveplot is a trivial compatibility wrapper for the print function, which saves the current plot to a disk file (§J.3). The saved freqplot plots are shown in Fig.7.3(a) and Fig.7.3(b).8.3

 [B,A] = ellip(4,1,20,0.5); % Design the lowpass filter [H,w] = freqz(B,A); % Compute its frequency response % Plot the frequency response H(w): % figure(1); freqplot(w,abs(H),'-k','Amplitude Response',... 'Frequency (rad/sample)', 'Gain'); saveplot('../eps/freqzDemoOne.eps'); figure(2); freqplot(w,angle(H),'-k','Phase Response',... 'Frequency (rad/sample)', 'Phase (rad)'); saveplot('../eps/freqzDemoTwo.eps'); % Plot frequency response in a "multiplot" like Matlab uses: % figure(3); plotfr(H,w/(2*pi)); saveplot('../eps/freqzdemo3.eps'); 

 Amplitude Response Phase Response

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