Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 344

frequency components and the high frequency components. The MATLAB list for the simulation is
shown in Program 8.11.
Program 8.11. MATLAB program for the digital audio equalizer.

close all; clear all
% Filter Coefficients (Butterworth type designed using the BLT)
B0 ¼ [0.0031954934 0 -0.0031954934]; A0 ¼ [1.0000000000 -1.9934066716 0.9936090132];
B1 ¼ [0.0063708102 0 -0.0063708102]; A1 ¼ [1.0000000000 -1.9864516324 0.9872583796];
B2 ¼ [0.0126623878 0 -0.0126623878]; A2 ¼ [1.0000000000 -1.9714693192 0.9746752244];
B3 ¼ [0.0310900413 0 -0.0310900413]; A3 ¼ [ 1.0000000000 -1.9181849043 0.9378199174];
B4 ¼ [0.0746111954 0.000000000 -0.0746111954];
A4 ¼ [1.0000000000 -1.7346085867 0.8507776092];
B5 ¼ [0.1663862883 0.0000000000 -0.1663862884];
A5 ¼ [1.0000000000 -1.0942477187 0.6672274233];
B6 ¼ [0.3354404899 0.0000000000 -0.3354404899];
A6 ¼ [1.0000000000 0.7131366534 0.3291190202];

[h0,f] ¼ freqz(B0,A0,2048,44100);
[h1,f] ¼ freqz(B1,A1,2048,44100);
[h2,f] ¼ freqz(B2,A2,2048,44100);
[h3,f] ¼ freqz(B3,A3,2048,44100);
[h4,f] ¼ freqz(B4,A4,2048,44100);
[h5,f] ¼ freqz(B5,A5,2048,44100);
[h6,f] ¼ freqz(B6,A6,2048,44100);
loglog(f,abs(h0),f,abs(h1), f,abs(h2), .
f,abs(h3),f,abs(h4),f,abs(h5),f,abs(h6));
xlabel( ' Frequency (Hz) ' );
ylabel( ' Filter Gain ' );grid
axis([10 10^5 10^(-6) 1]);
figure(2)
g0 ¼ 10;g1 ¼ 10;g2 ¼ 0;g3 ¼ 0;g4 ¼ 0;g5 ¼ 10;g6 ¼ 10;
p0 ¼ 0;p1 ¼ pi/14;p2 ¼ 2*p1;p3 ¼ 3*p1;p4 ¼ 4*p1;p5 ¼ 5*p1;p6 ¼ 6*p1;
n ¼ 0:1:20480; % Indices of samples

fs ¼ 44100;

% Sampling rate

x ¼ sin(2*pi*100*n/fs) þ sin(2*pi*200*n/fs þ p1) þ .

sin(2*pi*400*n/fs þ p2) þ sin(2*pi*1000*n/fs þ p3) þ .

sin(2*pi*2500*n/fs þ p4) þ sin(2*pi*6000*n/fs þ p5) þ .

sin(2*pi*15000*n/fs þ p6); % Generate test audio signals

y0 ¼ filter(B0,A0,x); % Bandpass filter 0

y1 filter(B1,A1,x); % Bandpass filter 1

y2 ¼ filter(B2,A2,x); % Bandpass filter 2
y3 ¼ filter(B3,A3,x); % Bandpass filter 3
y4 ¼ filter(B4,A4,x); % Bandpass filter 4
y5 ¼ filter(B5,A5,x); % Bandpass filter 5
y6 ¼ filter(B6,A6,x); % Bandpass filter 6
y ¼ g0.*y0 þ g1.*y1 þ g2.*y2 þ g3.*y3 þ g4.*y4 þ g5.*y5 þ g6.*y6 þ x; % Equalizer output
N ¼ length(x);
Axk ¼ 2*abs(fft(x))/N;Axk(1) ¼ Axk(1)/2; % One-sided amplitude spectrum of the input
f ¼ [0:N/2]*fs/N;

¼