![Bandpass Filter
close all;
clear all;
r1 = 0.9;
r2 = 0.88;
r3=0.9;
theta1 = pi/5;
theta2 = 3*pi/10;
theta3=4*pi/10;
p1 = r1*cos(theta1) + i*r1*sin(theta1);
p2 = r1*cos(theta2) + i*r2*sin(theta2);
p3 = r3*cos(theta3) + i*r3*sin(theta3);
p2 = r2*cos(theta2) + i*r2*sin(theta2);
!aroots = [p1,conj(p1),p2,conj(p2), p3, conj(p3)];
aroots = [p2,conj(p2), p3, conj(p3)];
a = poly(aroots);
b = [1 zeros(1,18) -1];
b1 = [1];
[h,w] = freqz(b1,a);
freqzplot(h,w, 'mag');
figure;
freqzplot(h,w,'squared');
( )( ) ( )( )[ ]
( ) ( )
( ) ( )[ ]2121
4.0
21
3
3.0
21
2
1111
)4.0cos(219.0)3.0cos(219.0/1
cos219.0cos219.0/1
119.0119.0/1)(
32
3322
−−−−
=
−−
=
−−
−−−+−−−+
+−+−=
+−+−=
−−−−=
zzzz
zzzz
zezezezezH jjjj
ππ
ωω
πωπω
ωωωω](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-2-320.jpg)
![Kaiser Bessel Window
clear all;
close all;
N=61;
w31 = window(@kaiser,N,1);
w33 = window(@kaiser,N,3);
w35 = window(@kaiser,N,5);
w37 = window(@kaiser,N,7);
plot(1:N,[w31, w33, w35, w37]); axis([1 N 0 1]);
legend('beta=1','beta = 3', 'beta=5', 'beta=7');
figure;
a=[1];
[fw31,f] = freqz(w31,a);
[fw33,f] = freqz(w33,a);
[fw35,f] = freqz(w35,a);
[fw37,f] = freqz(w37,a);
freqzplot([fw31,fw33,fw35,fw37],f, 'mag');
legend('beta=1','beta = 3', 'beta=5', 'beta=7');](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-3-320.jpg)
![Time Domain Windows
clear all;
close all;
N=61;
w = window(@blackmanharris,N);
w1 = window(@hamming,N);
w2 = window(@gausswin,N,2.5);
w3 = window(@kaiser,N,5);
w4 = window(@tukeywin,N,0.5);
plot(1:N,[w1,w3,w4]); axis([1 N 0 1]);
legend('Hamming','Kaiser', 'Tukey');
figure;
a=[1];
[fw,f] = freqz(w,a);
[fw1,f] = freqz(w1,a);
[fw2,f] = freqz(w2,a);
[fw3,f] = freqz(w3,a);
[fw4,f] = freqz(w4,a);
freqzplot([fw1,fw3,fw4],f, 'mag');
legend('Hamming','Kaiser', 'Tukey');](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-4-320.jpg)
![Notch Filters
clear all;
close all;
a = [1 -1.2726 0.81];
b = [1 -1.414 1];
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Pole-zero Notch Filter - Mag');
figure;
freqzplot(H,W);
title ('Pole-zero Notch Filter - dB');
a1 = [1];
b1 = [1 -1.414 1];
[H1, W] = freqz(b1,a1);
figure;
freqzplot(H1,W,'linear');
title ('All zero Notch Filter - Mag');
figure;
freqzplot(H1,W);
title ('All zero Notch Filter - dB');
1 2
3 4](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-6-320.jpg)
![Resonators
clear all;
close all;
r = 0.99;
theta = pi/4;
a = [1 -2*r*theta r^2];
b = 1;
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Resonator r=0.99, theta = pi/4 - Mag');
figure;
freqzplot(H,W);
title (' Resonator r=0.99, theta = pi/4- dB');
r = 0.95;
theta = pi/4;
a = [1 -2*r*theta r^2];
b = 1;
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Resonator r=0.95, theta = pi/4 - Mag');
figure;
freqzplot(H,W);
title (' Resonator r=0.95, theta = pi/4- dB');
r = 0.99;
theta = pi/4;
a = [1 -2*r*theta r^2];
b = [1 0 -1]
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Pole-zero Resonator r=0.99, theta = pi/4 - Mag');
figure;
freqzplot(H,W);
title ('Pole-zero Resonator r=0.99, theta = pi/4- dB');
r = 0.9;
theta = pi/4;
a = [1 -2*r*theta r^2];
b = 1;
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Resonator r=0.9, theta = pi/4 - Mag');
figure;
freqzplot(H,W);
title (' Resonator r=0.9, theta = pi/4- dB');
r = 1.0;
theta = pi/4;
a = [1 -2*r*theta r^2];
b = 1;
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Oscillator, theta = pi/4 - Mag');
figure;
freqzplot(H,W);
title ('Oscillator, theta = pi/4- dB');
1](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-7-320.jpg)
![Comb Filters
clear all;
close all;
a = [1 -1];
b = [1 0 0 0 0 0 0 0 0 0 0 -1];
b = b/11;
[H, W] = freqz(b,a);
figure;
freqzplot(H,W,'linear');
title ('Comb Filter M=10 - Mag');
figure;
freqzplot(H,W);
title ('Comb Filter M=10 - dB');
bz = zeros (1,54);
a1 = [1 0 0 0 0 -1];
b1 = [1 [bz] -1];
[H, W] = freqz(b1,a1);
figure;
freqzplot(H,W,'linear');
title ('LM Comb Filter L = 5 M=10 - Mag');
figure;
freqzplot(H,W);
title ('LM Comb Filter L = 5 M=10 - dB');
1 2
3 4](https://image.slidesharecdn.com/matlabdspexamples-160302180401/85/Matlab-dsp-examples-9-320.jpg)
Matlab dsp examples
- 1. MATLAB DSP Programs Raja Rajasakeran Venkat Peddigari Pete Bernardin
- 2. Bandpass Filter close all; clear all; r1 = 0.9; r2 = 0.88; r3=0.9; theta1 = pi/5; theta2 = 3*pi/10; theta3=4*pi/10; p1 = r1*cos(theta1) + i*r1*sin(theta1); p2 = r1*cos(theta2) + i*r2*sin(theta2); p3 = r3*cos(theta3) + i*r3*sin(theta3); p2 = r2*cos(theta2) + i*r2*sin(theta2); !aroots = [p1,conj(p1),p2,conj(p2), p3, conj(p3)]; aroots = [p2,conj(p2), p3, conj(p3)]; a = poly(aroots); b = [1 zeros(1,18) -1]; b1 = [1]; [h,w] = freqz(b1,a); freqzplot(h,w, 'mag'); figure; freqzplot(h,w,'squared'); ( )( ) ( )( )[ ] ( ) ( ) ( ) ( )[ ]2121 4.0 21 3 3.0 21 2 1111 )4.0cos(219.0)3.0cos(219.0/1 cos219.0cos219.0/1 119.0119.0/1)( 32 3322 −−−− = −− = −− −−−+−−−+ +−+−= +−+−= −−−−= zzzz zzzz zezezezezH jjjj ππ ωω πωπω ωωωω
- 3. Kaiser Bessel Window clear all; close all; N=61; w31 = window(@kaiser,N,1); w33 = window(@kaiser,N,3); w35 = window(@kaiser,N,5); w37 = window(@kaiser,N,7); plot(1:N,[w31, w33, w35, w37]); axis([1 N 0 1]); legend('beta=1','beta = 3', 'beta=5', 'beta=7'); figure; a=[1]; [fw31,f] = freqz(w31,a); [fw33,f] = freqz(w33,a); [fw35,f] = freqz(w35,a); [fw37,f] = freqz(w37,a); freqzplot([fw31,fw33,fw35,fw37],f, 'mag'); legend('beta=1','beta = 3', 'beta=5', 'beta=7');
- 4. Time Domain Windows clear all; close all; N=61; w = window(@blackmanharris,N); w1 = window(@hamming,N); w2 = window(@gausswin,N,2.5); w3 = window(@kaiser,N,5); w4 = window(@tukeywin,N,0.5); plot(1:N,[w1,w3,w4]); axis([1 N 0 1]); legend('Hamming','Kaiser', 'Tukey'); figure; a=[1]; [fw,f] = freqz(w,a); [fw1,f] = freqz(w1,a); [fw2,f] = freqz(w2,a); [fw3,f] = freqz(w3,a); [fw4,f] = freqz(w4,a); freqzplot([fw1,fw3,fw4],f, 'mag'); legend('Hamming','Kaiser', 'Tukey');
- 5. DFT of Square Waves, 3 Duties close all; clear all; x = ones(1,16); y = fft(x,16); my = abs(y)/16; ay = angle(y); stem(my); figure; y1 = fft (x,32)/16; my1 = abs(y1); stem(my1); y2= fft (x,128); figure; stem (abs(y2)); 100% Duty 50% Duty 12.5% Duty
- 6. Notch Filters clear all; close all; a = [1 -1.2726 0.81]; b = [1 -1.414 1]; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Pole-zero Notch Filter - Mag'); figure; freqzplot(H,W); title ('Pole-zero Notch Filter - dB'); a1 = [1]; b1 = [1 -1.414 1]; [H1, W] = freqz(b1,a1); figure; freqzplot(H1,W,'linear'); title ('All zero Notch Filter - Mag'); figure; freqzplot(H1,W); title ('All zero Notch Filter - dB'); 1 2 3 4
- 7. Resonators clear all; close all; r = 0.99; theta = pi/4; a = [1 -2*r*theta r^2]; b = 1; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Resonator r=0.99, theta = pi/4 - Mag'); figure; freqzplot(H,W); title (' Resonator r=0.99, theta = pi/4- dB'); r = 0.95; theta = pi/4; a = [1 -2*r*theta r^2]; b = 1; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Resonator r=0.95, theta = pi/4 - Mag'); figure; freqzplot(H,W); title (' Resonator r=0.95, theta = pi/4- dB'); r = 0.99; theta = pi/4; a = [1 -2*r*theta r^2]; b = [1 0 -1] [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Pole-zero Resonator r=0.99, theta = pi/4 - Mag'); figure; freqzplot(H,W); title ('Pole-zero Resonator r=0.99, theta = pi/4- dB'); r = 0.9; theta = pi/4; a = [1 -2*r*theta r^2]; b = 1; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Resonator r=0.9, theta = pi/4 - Mag'); figure; freqzplot(H,W); title (' Resonator r=0.9, theta = pi/4- dB'); r = 1.0; theta = pi/4; a = [1 -2*r*theta r^2]; b = 1; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Oscillator, theta = pi/4 - Mag'); figure; freqzplot(H,W); title ('Oscillator, theta = pi/4- dB'); 1
- 9. Comb Filters clear all; close all; a = [1 -1]; b = [1 0 0 0 0 0 0 0 0 0 0 -1]; b = b/11; [H, W] = freqz(b,a); figure; freqzplot(H,W,'linear'); title ('Comb Filter M=10 - Mag'); figure; freqzplot(H,W); title ('Comb Filter M=10 - dB'); bz = zeros (1,54); a1 = [1 0 0 0 0 -1]; b1 = [1 [bz] -1]; [H, W] = freqz(b1,a1); figure; freqzplot(H,W,'linear'); title ('LM Comb Filter L = 5 M=10 - Mag'); figure; freqzplot(H,W); title ('LM Comb Filter L = 5 M=10 - dB'); 1 2 3 4
- 10. Welch Periodogram PSD close all; clear all; t = 0:.001:4.096; x = sin(2*pi*50*t) + sin(2*pi*120*t); stdev = 2; y = x + stdev*randn(size(t)); figure; plot(y(1:50)) title('Noisy time domain signal') FS = 1000.; % Sampling Rate % 1 section NFFT = 4096; Noverlap = 0 figure; pwelch(y, 4096, Noverlap, NFFT, FS) % 16 overlapping sections NFFT = 512; Noverlap = 256 figure; pwelch(y, 512, Noverlap, NFFT, FS) % 32 overlapping sections NFFT = 256; Noverlap = 128 figure; pwelch(y, 256, Noverlap, NFFT, FS) ¼ Hz Res 2 Hz Res 4 Hz Res Time 1 2 43
- 11. Discrete Fourier Transform (DFT) Forward Transform: for k=0,1,2,…,N-1 Inverse Transform: for n=0,1,2,…,N-1 ----------------------------------------------------------------------------------------------------------- N=8; % MATLAB “DISCRETE FOURIER TRANSFORM” PROGRAM w0 = 2*pi/N; K0 =3; w=w0*K0*(0:N-1); Data = complex(cos(w),sin(w)); % Data = ej2πnKo/N for k =1:N accum=complex(0,0); for n=1:N A = w0*(n-1)*(k-1); Twiddle=complex(cos(A),-sin(A)); %Twiddle = e-j2πnk/N accum = accum+Data(n)*Twiddle; % X(k)= Σej2πnKo/N e-j2πnk/N end % "n" is Time index MAGXk=abs(accum) % Output the Magnitude of the DFT =N @ k=K0 end % "k" is the Frequency index