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Chapter 11 Analog and Digital Filters102nd Order Butterworth Low-Pass Filter ResponseFigure 11.20. Plot for the VCVS low−pass filter of Example 11.6We have used the MATLAB buttap function earlier to aid us in the design of Butterworth filterswith the cutoff frequency normalized to 1 rad ⁄ s. We can also use the bode function to displayboth the (asymptotic) magnitude and phase plots. The following script will produce the Bodemagnitude and phase plots for a two−pole Butterworth low-pass filter.[z,p,k]= buttap(2);% Specify a two−pole filter;...[b,a]=zp2tf(z,p,k);% Display in polynomial rational form;...w=0:0.01:4; [mag,phase]=bode(b,a,w);...b,a% Display b and a coefficientsb =a =|Vout/Vin| (dB)-10-20-30-40-50-60-700 0 11.0000 1.4142 1.0000num=[0 0 1]; den=[1 sqrt(2) 1];...bode(num,den); title('Butterworth 2nd Order Low−Pass Filter'); gridThe Bode plots are shown in Figure 11.21. The frequency is displayed infrequency normalized to 1 rad ⁄ s.and the cutoffWe can also display the Bode plots with the frequency specified in Hz. This can be done with theMATLAB script below.h=bodeplot(tf(num,den));...setoptions(h,'FreqUnits', 'Hz'); grid0-8010 0 10 1 10 2 10 3 10 4 10 5Frequency Hzrad ⁄ secThe Bode plots with the frequency specified in Hz are shown in Figure 11.22.11−24Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications