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Highlights from
Digital Signal Processing Using MATLAB

Digital Signal Processing Using MATLAB

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21 Aug 2002 (Updated )

Companion Software

ex081100.m
% Chapter 8: Example 8.11

%            Impulse Invariance Transformation

%                  Butterworth Lowpass Filter Design

%

% Digital Filter Specifications:

wp = 0.2*pi;                         % digital Passband freq in Hz

ws = 0.3*pi;                         % digital Stopband freq in Hz

Rp = 1;                              % Passband ripple in dB

As = 15;                             % Stopband attenuation in dB



% Analog Prototype Specifications: Inverse mapping for frequencies

T = 1;                               % Set T=1

OmegaP = wp * T;                     % Prototype Passband freq

OmegaS = ws * T;                     % Prototype Stopband freq

ep = sqrt(10^(Rp/10)-1);             % Passband Ripple parameter

Ripple = sqrt(1/(1+ep*ep));          % Passband Ripple

Attn = 1/(10^(As/20));               % Stopband Attenuation



% Analog Butterworth Prototype Filter Calculation:

[cs,ds] = afd_butt(OmegaP,OmegaS,Rp,As);

%%*** Butterworth Filter Order =  6 



% Impulse Invariance transformation:

[b,a] = imp_invr(cs,ds,T);

[C,B,A] = dir2par(b,a)

%%C =  []

%%B = 1.8557   -0.6304

%%   -2.1428    1.1454

%%    0.2871   -0.4466

%%A = 1.0000   -0.9973    0.2570

%%    1.0000   -1.0691    0.3699

%%    1.0000   -1.2972    0.6949



% Plotting

figure(1); subplot(1,1,1)

[db,mag,pha,grd,w] = freqz_m(b,a);

subplot(2,2,1); plot(w/pi,mag); title('Magnitude Response')

xlabel('frequency in pi units'); ylabel('|H|'); axis([0,1,0,1.1])

set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);

set(gca,'YTickmode','manual','YTick',[0,Attn,Ripple,1]); grid

subplot(2,2,3); plot(w/pi,db); title('Magnitude in dB');

xlabel('frequency in pi units'); ylabel('decibels'); axis([0,1,-40,5]);

set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);

set(gca,'YTickmode','manual','YTick',[-50,-15,-1,0]); grid

set(gca,'YTickLabelMode','manual','YTickLabels',['50';'15';' 1';' 0'])

subplot(2,2,2); plot(w/pi,pha/pi); title('Phase Response')

xlabel('frequency in pi units'); ylabel('pi units'); axis([0,1,-1,1]);

set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);

set(gca,'YTickmode','manual','YTick',[-1,0,1]); grid

subplot(2,2,4); plot(w/pi,grd); title('Group Delay')

xlabel('frequency in pi units'); ylabel('Samples'); axis([0,1,0,10])

set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);

set(gca,'YTickmode','manual','YTick',[0:2:10]); grid



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