dsp_lab_manual_matlab_ankit

D.S.P. Lab Book Submitted by:

Ankit A. Bhurane [2009MEC001]

Shri Guru Gobind Singhji Institute of Engineering & Technology,

Nanded, Maharashtra.

CONTENTS

MATLAB® programs:

1. Basic discrete-time sequences……………………………………………………... 1

2. Decomposition of real signal into even & odd components………………………. 5

3. Range of digital frequency of a sinusoid…………………………………………... 7

4. Sampling Theorem

a) Verification of sampling theorem……………………………………………... 9

b) Demonstrate sampling theorem (alternative)………………………………….. 11

5. Convolution

a) 1-D linear convolution & deconvolution using Formula……………………… 13

b) 1-D linear and circular convolution & deconvolution using

Matrix Multiplication………………………………………………………….. 14

c) 1-D circular convolution from linear convolution…………………………….. 15

6. Discrete Fourier Transform

a) N-point Discrete Fourier Transform (DFT) & Inverse Discrete Fourier

Transform (IDFT)……………………………………………………………... 17

b) Getting IDFT from DFT………………………………………………………. 18

7. Convolution Theorem……………………………………………………………… 20

8. Impulse response & frequency response of an IIR & FIR systems………………… 21

9. Gibbs Phenomenon…………………………………………………………………. 23

10. FIR filter design using windowing…………………………………………………. 25

11. Butterworth IIR filter design using bilinear transform……………………………… 27

12. Filtering of a signal using FIR filter……………………………………………….. 29

13. Filtering of a signal using IIR filter………………………………………………… 31

Appendix

S.G.G.S.I..E.T., Nanded. D.S.P. Lab Book

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Lab 1: Basic discrete-time sequences.

Matlab code:

%% Copyright Notice

% ========================================================================= % DSP Lab 1: Matlab code for plotting basic discrete time sequences. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================

%% Clear previous Data (if required)

clc; close all; clear all;

%% Define desired Signals

x = -10:10; % Time axis

y1 = zeros(1,21); y1(1,11) = 1; % Unit Impulse y2 = zeros(1,21); y2(1,11:21) = 1; % Unit Step y3 = 0:10; % Unit Ramp y4 = exp(0:2*pi/10:2*pi); % Exponential (Increasing) y5 = exp(-(0:2*pi/10:2*pi)); % Exponential (Decreasing) y6 = sin(0:2*pi/10:2*pi); % Sinusoid

%% Plot desired signals

subplot(3,2,1); stem(x,y1); title('Unit Impulse'); subplot(3,2,2); stem(x,y2); title('Unit Step'); subplot(3,2,3); stem(y3,y3); title('Unit Ramp'); subplot(3,2,4); stem(y3,y4); title('Exponential Increasing'); subplot(3,2,5); stem(y3,y5); title('Exponential Decreasing'); subplot(3,2,6); stem(y3,y6); title('Sinusoid');

% ================================ END ====================================


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Output:

Lab 2: Decomposition of real signal into even & odd components.

Matlab code:

%% Copyright Notice


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% ========================================================================= % DSP Lab 2: Matlab code for decomposition of real signal into even & odd. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. %-------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================


clc; close all; clear all;

x = -10:10; % Time axis y = zeros(1,21); y(1,11:21) = 1; % Step Signal e = (y + fliplr(y))/2; % Even decomposition o = (y - fliplr(y))/2; % Odd decomposition

%% Plot desired Signals

subplot(5,1,1); stem(x,y); title('Original signal'); % Plot original signal subplot(5,1,2); stem(x,fliplr(y)); title('Fliped signal'); % Its Fliped ver subplot(5,1,3); stem(x,e); title('Even Decomposition'); subplot(5,1,4); stem(x,o); title('Odd Decomposition'); subplot(5,1,5); stem(x,e+o); title('Reconstructed/ Synthesized signal');

% ================================ END ====================================

Output:


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Lab 3: Range of digital frequency of a sinusoid.

Matlab code:

%% Copyright Notice

% ========================================================================= % DSP Lab 3: Matlab code to verify the range of digital frequency. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================


clc; clear all; close all;

%% Define required Parameters & Plot Signals

w = 0:pi/4:2*pi; % Omega ( For unique sequences maximium value is pi ) n = 0:49; % Number of samples = 50 t = 0; % Theta for k = 1:9 subplot(3,3,k); stem(cos(w(k)*n + t)); title(strcat('w =',num2str(w(k)))); end

% ================================ END ====================================


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Output:


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Lab 4: Sampling theorem.

(a) Verify sampling theorem.

(b) Demonstrate sampling theorem (alternate).

Matlab code:

(a)

%% Copyright Notice

% ========================================================================= % DSP Lab 4(a): Maltab code to verify sampling theorem ( Nyquist Rate ). % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Specifications

F = 0:5:45; % Frequency varied from 0 to 45 Hz Fs = 50; % Sampling Frequency n = 0:Fs; % Sampling instant f = -Fs/2:Fs/2; % Frequency Axis (Symmetric)

%% Calculate & Plot desired Signals

for k = 1:size(F,2) y = cos(2*pi*F(k)/Fs*n); figure(1); subplot(5,2,k); plot(n,y); xlabel('Time(s)'); title(strcat('F =',num2str(F(k)),'Hz, Fs = 50 Hz')); figure(2); subplot(5,2,k); stem(f,abs(fftshift(fft(y)))); xlabel('Frequency(Hz)'); end

% ================================ END ====================================


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Output:


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(b)

%% Copyright Notice

% ========================================================================= % DSP Lab 4(b): Maltab code to demostrate sampling theorem( Nyquist Rate ). % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Specifications

Fc = 1; Fs1 = 100*Fc; Fs2 = 1.2*Fc; Fs3 = 2*Fc; Fs4 = 10*Fc; t1 = 0:1/Fs1:10; t2 = 0:1/Fs2:10; t3 = 0:1/Fs3:10; t4 = 0:1/Fs4:10; % 10Sec

%% Signals

s1 = cos(2*pi*Fc*t1); % Original signal sampled at very high rate (100*Fs) s2 = cos(2*pi*Fc*t2); % Original signal sampled at SR < 2*Fc (SR = Fc) s3 = cos(2*pi*Fc*t3); % Original signal sampled at SR = 2*Fc s4 = cos(2*pi*Fc*t4); % Original signal sampled at SR > 2*Fc (SR = 10*Fc)


subplot(311); plot(t1,s1,'r',t2,s2,'b*-'); title('For SR < 2*Fc'); subplot(312); plot(t1,s1,'r',t3,s3,'b*-'); title('For SR = 2*Fc'); subplot(313); plot(t1,s1,'r',t4,s4,'b*-'); title('For SR > 2*Fc');

% ================================ END ====================================


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Output:


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Lab 5: Convolution.

(c) 1-D linear convolution & deconvolution using Formula.

(d) 1-D linear and circular convolution & deconvolution using Matrix Multiplication.

(e) 1-D circular convolution from linear convolution.

Matlab code:

(a)

%% Copyright Notice

% ========================================================================= % DSP Lab 5(a): Matlab code for 1-D linear convolution & deconvolution % (using formula). % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Parameters

x = [1 2 3 4]; % First Signal h = [5 6 7 8]; % Second Signal

%% Calculate Linear Convolution Length

l1 = length(x); l2 = length(h); l = l1+l2-1;

x = [x zeros(1,l2-1)]; % Zero Padding h = [h zeros(1,l1-1)]; % Zero Padding y = zeros(1,l);

%% Linear Convolution

for i = 1:1:l for k = 1:1:i y(i) = y(i)+x(k)*h(i+1-k);


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end end disp(['Convolution: ', num2str(y)]);

%% Linear Deconvolution

x_r = zeros(1,l1); x_r(1) = y(1)/h(1); for i = 2:1:l1 for k = 1:1:i-1 x_r(i) = x_r(i)+x(k)*h(i+1-k); end x_r(i) = (y(i)-x_r(i))/h(1); end disp(['Deconvolution: ', num2str(x_r)]);

% ================================ END ====================================

Output:

Convolution: 5 16 34 60 61 52 32

Deconvolution: 1 2 3 4

(b)

%% Copyright Notice

% ========================================================================= % DSP Lab 5(b): Matlab code for 1-D linear & circular convolution ( using % matrix multiplication method ). % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Parameters


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%% Calculate Convolution Length

l1 = length(x); l2 = length(h); l = l1+l2-1; m = max(l1,l2);

%% Circular Convolution

x1 = [x zeros(1,m-l1)]; h1 = [h zeros(1,m-l2)];

p1 = zeros(m,m); for i = 1:m p1(:,i) = circshift(x1',i-1); end cir = p1*h1'; disp(['The circular convolution is: ', num2str(cir')]);


x2 = [x zeros(1,l-l1)]; h2 = [h zeros(1,l-l2)];

p2 = zeros(l,l); for i = 1:l p2(:,i) = circshift(x2',i-1); end lin = p2*h2'; disp(['The linear convolution is: ', num2str(lin')]);

% ================================ END ====================================

Output:

The circular convolution is: 66 68 66 60

The linear convolution is: 5 16 34 60 61 52 32

(c) %% Copyright Notice

% ========================================================================= % DSP Lab 5(c): Matlab code for getting circular convolution result from % linear convolution using pad-add method. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original


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% author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Parameters


%% Calculate Convolution Length

l1 = length(x); l2 = length(h); m = max(l1,l2);


lin_c = conv(x,h); disp(['The linear convolution is: ', num2str(lin_c)]);

%% Padd-Add

temp = [lin_c zeros(1,2*m-(l1+l2-1))]; % Zero Padd circ_c = temp(1,1:m)+temp(1,m+1:end); % Add disp(['The circular convolution is: ', num2str(circ_c)]);

% ================================ END ====================================

Output:

The linear convolution is: 5 16 34 60 61 52 32

The circular convolution is: 66 68 66 60


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Lab 6: Discrete Fourier Transform.

(a) N-point Discrete Fourier Transform (DFT) & Inverse Discrete Fourier Transform

(IDFT).

(b) Getting IDFT from DFT.

Matlab code:

(a)

%% Copyright Notice

% ========================================================================= % DSP Lab 6(a): Matlab code for N-point DFT & IDFT. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Parameters

x = [1 2 3 4]; % Input Signal in Time Domain N = 5; % Desired Length of DFT l = length(x); x = [x zeros(1,N-l)];

%% Discrete Fourier Transform

f = zeros(1,N); k = 0:N-1; for n = 0:N-1 f(k+1) = f(k+1) + x(n+1)*exp(-1j*2*pi*k*n/N); end disp('DFT is: '); disp(f);

%% Inverse Discrete Fourier Transform

r = zeros(1,N); n = 0:N-1; for k = 0:N-1


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r(n+1) = r(n+1) + f(k+1)*exp(1j*2*pi*k*n/N); end r(n+1) = r(n+1)/N; disp('IDFT is: '); disp(r);

% ================================ END ====================================

Output:

DFT is:

10.0000 -4.0451 - 1.3143i 1.5451 - 2.1266i

1.5451 + 2.1266i -4.0451 + 1.3143i

IDFT is:

1.0000 - 0.0000i 2.0000 3.0000 + 0.0000i

4.0000 + 0.0000i 0.0000 + 0.0000i

(b) %% Copyright Notice

% ========================================================================= % DSP Lab 6(b): Maltab code to find IDFT using DFT. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Calculations

x = [1 2 3 4]; % Signal in Time Domain dft = fft(x); disp(['The DFT is: ', num2str(dft)]); idft = (1/size(x,2))*conj(fft(conj(dft))); % Algorithm disp(['The IDFT using DFT is: ', num2str(idft)]);


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% ================================ END ====================================

Output: The DFT is: 10+0i -2+2i -2+0i -2-2i

The IDFT using DFT is: 1 2 3 4


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Lab 7: Convolution Theorem.

Matlab code: %% Copyright Notice

% ========================================================================= % DSP Lab 7: Maltab code to verify convolution theorem. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Calculations

x1 = [1 2 3 4]; % First Signal x2 = [5 6 7 8]; % Second Signal f1 = fft(x1); f2 = fft(x2); disp(['Conv in TD: ',num2str(cconv(x1,x2,max(length(x1),length(x2))))]); disp(['Inverse of their multiplication in FD: ',num2str(ifft(f1.*f2))]);

% ================================ END ====================================

Output: Conv in TD: 66 68 66 60

Inverse of their multiplication in FD: 66 68 66 60


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Lab 8: Impulse response & frequency response of an IIR & FIR systems.


% ========================================================================= % DSP Lab 8: Matlab code to find Impulse Responce & Frequency Responce of % an IIR & FIR systems. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% IIR

num_iir = [0.5 1 0.5]; den_iir = [1 0 0.5]; impz(num_iir,den_iir,50); title('Impulse Responce of IIR filter'); figure; freqz(num_iir,den_iir); title('Frequency Responce of IIR filter');

%% FIR

num_fir = [0.5 0.5 0.5]; den_fir = 1; figure; impz(num_fir,den_fir,50); title('Impulse Responce of FIR filter'); figure; freqz(num_fir,den_fir); title('Frequency Responce of FIR filter');

% ================================ END ====================================


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Output:


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Lab 9: Gibbs Phenomenon.

Matlab code:

%% Copyright Notice

% ========================================================================= % DSP Lab 9: Matlab code to demonstrate Gibbs phenomenon. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Frequency and Time Domain of Ideal Low Pass Filter

H = zeros(1,101); H(1,48:54) = 1; % Frequency Domain h = abs(fftshift(ifft(H))); % Time Domain

%% Frequency and Time Domain of Ideal Rectangular Window

w = zeros(1,101); w(1,36:66) = 1; W = abs(fftshift(fft(w)));

m = h.*w; M = abs(fftshift((fft(m))));

%% Plot the Desired Signals

subplot(321); stem(-50:50,h); title('Its TD representation'); subplot(322); stem(-50:50,H); title('Ideal LP frequency Responce'); subplot(323); stem(-50:50,w); title('Ideal Rectangular window in TD'); subplot(324); stem(-50:50,W); title('Its FD representation'); subplot(325); stem(-50:50,m); title('Windowed Fourier coefficients in TD'); subplot(326); stem(-50:50,M); title('Its FD representation');

% ================================ END ====================================


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Output:


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Lab 10: FIR filter design using windowing.

Matlab code:

%% Copyright Notice

% ========================================================================= % DSP Lab 10: Matlab code to design FIR filter using windowing. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



L=11; % Length of Filter Wc = 0.5; % Normalized cutoff frequency

%% Calculating desired Filter Coefficients

b1 = fir1(L-1, Wc, 'low', rectwin(L)); b2 = fir1(L-1, Wc, 'low', bartlett(L)); b3 = fir1(L-1, Wc, 'low', hamming(L)); b4 = fir1(L-1, Wc, 'low', hanning(L)); b5 = fir1(L-1, Wc, 'low', blackman(L));

%% Calculate their Frequency Responce

[h1,w] = freqz(b1); h2 = freqz(b2); h3 = freqz(b3); h4 = freqz(b4); h5 = freqz(b5);


w = w/pi; % Normalize Frequency Axis

plot(w, 20*log(abs(h1)), 'b'); hold on; plot(w, 20*log(abs(h2)), 'g');


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plot(w, 20*log(abs(h3)), 'r'); plot(w, 20*log(abs(h4)), 'c'); plot(w, 20*log(abs(h5)), 'k');

legend('Rectwin','Bartlett','Hamming','Hanning','Blackman'); xlabel('Normalized Frequency'); ylabel('Magnitude (dB)'); grid on;

% ================================ END ====================================

Output:


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Lab 11: Butterworth IIR filter design using bilinear transform.


% ========================================================================= % DSP Lab 11: Matlab code to design Butterworth IIR filter using Biliner % Transform. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Filter Specifications

Fp = 1000; % Passband Frequency in Hertz Fs = 350; % Stopband Frequency in Hertz Ap = 3; % Passband Attenuation in dB As = 10; % Stopband Attenuation in dB SR = 5000; % Sampling Rate in Samples/Sec ftype = 'high'; % Filter Type Wp = 2*Fp/SR; Ws = 2*Fs/SR; % Passband & Stopband Frequencies (pi not reqd)

%% Design required Filter

[n,Wn] = buttord(Wp,Ws,Ap,As); [b,a] = butter(n,Wn,ftype);

%% Plot its Frequency Responce

freqz(b,a); title('Frequency Resonce');

% ================================ END ====================================


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Output:


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Lab 12: Filtering of a signal using FIR filter.


% ========================================================================= % DSP Lab 12: Matlab code for filtering of a signal using FIR filter. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Given Specifications

SR = 500; % If the sampling freq is changed, change the order accordingly n = 0:SR-1; F1 = 5; F2 = 50; % Frequencies of two signals Filt_Ord = 20; % Preferably Even (because all filter can be implemented) Filt_Len = Filt_Ord + 1;

x1 = cos(2*pi*F1/SR*n); % First sinusoid signal x2 = cos(2*pi*F2/SR*n); % Second sinusoid signal x = x1+x2; % Added signal

F = (F1 + F2)/2; % Average frequency for cutoff c = F/SR; % Cutoff Frequency

%% Filter Design

bl = fir1(Filt_Ord,c,'low',rectwin(Filt_Len)); % Low pass filtered signal bh = fir1(Filt_Ord,c,'high',rectwin(Filt_Len)); % High pass filtered signal

%% Filtering (Convolving)

fl = cconv(bl,x,SR); fh = cconv(bh,x,SR);


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% Alternate Method 2 % fl = filter(bl,1,x); % fh = filter(bh,1,x);

%% Plot Desired Signals

subplot(511); plot(n/SR,x1); title('10 Hz Signal'); subplot(512); plot(n/SR,x2); title('50 Hz Signal'); subplot(513); plot(n/SR,x); title('10 Hz + 50 Hz Signal'); subplot(514); plot(n/SR,fl); axis([0 1 -1 1]); title('Low pass FIR filtered signal (10 Hz)'); subplot(515); plot(n/SR,fh); axis([0 1 -1 1]); title('High pass FIR filtered Signal (50 Hz)');

% ================================ END ====================================

Output:


Ankit A. Bhurane 31

Lab 13: Filtering of signal using IIR filter


% ========================================================================= % DSP Lab 13: Matlab code for filtering of a signal using IIR filter. % Code By: Ankit A. Bhurane ( [email protected] ) % Last Updated: 25 April 2011 % ========================================================================= % Copyright © 2011 Ankit A. Bhurane % All Rights Reserved. % ------------------------------------------------------------------------- % Permission to use, copy, modify, distribute or sell this software and its % documentation for educational and research purposes only and without fee % is hereby granted, provided that this copyright notice and the original % author's name appear on all copies and supporting documentation. This % program shall not be used, rewritten, or adapted as the basis of a % commercial software or hardware product without first obtaining % permission of the author. The author make no representations about the % suitability of this software for any purpose. It is provided "as is" % without express or implied warranty. % ------------------------------------------------------------------------- % You can get this code from http://www.ankitbhurane.co.nr % or with a request to: [email protected] % =============================== START ===================================



%% Given Specifications

SR = 500; % If the sampling freq is changed, change the order accordingly n = 0:SR-1; F1 = 5; F2 = 50; % Frequencies of two signals Filt_Ord = 20; % Filter Order Preferably Even (coz all filters can be

implemented) Filt_Len = Filt_Ord + 1; % Filter Length

x1 = cos(2*pi*F1/SR*n); % First sinusoid signal x2 = cos(2*pi*F2/SR*n); % Second sinusoid signal x = x1+x2; % Added signal

F = (F1 + F2)/2; % Average frequency for cutoff c = F/SR; % Cutoff Frequency

%% Filter Design

[o,Wn] = buttord((2*F1/SR),(2*F2/SR),3,30); [bl,al] = butter(o,Wn,'low'); [bh,ah] = butter(o,Wn,'high');

%% Filtering (Convolving)

fl = cconv(impz(bl,al,300),x',SR); % f = deconv(conv(x,b),a); % filter uses

this logic.


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fh = cconv(impz(bh,ah,300),x',SR);

% Alternate Method 2 % fl = filter(bl,al,x); % fh = filter(bh,ah,x);

% Alternate Method 3 % fl = deconv(conv(x,bl),al); % 'filter' function uses this logic. % fh = deconv(conv(x,bh),ah); % 'filter' function uses this logic.

%% Plot Desired Signals

subplot(511); plot(n/SR,x1); title('10 Hz Signal'); subplot(512); plot(n/SR,x2); title('50 Hz Signal'); subplot(513); plot(n/SR,x); title('10 Hz + 50 Hz Signal'); subplot(514); plot(n/SR,fl); axis([0 1 -1 1]); title('Low pass FIR filtered signal (10 Hz)'); subplot(515); plot(n/SR,fh); axis([0 1 -1 1]); title('High pass FIR filtered Signal (50 Hz)');

% ================================ END ====================================

Output:

APPENDIX

+ Plus

- Minus

* Matrix multiplication

.* Array multiplication

^ Matrix power

.^ Array power

kron Kronecker tensor product

\ Backslash or left division

/ Slash or right division

./ and .\ Array division, right and left

: Colon

( ) Parentheses

[ ] Brackets

{} Curly braces

. Decimal point

... Continuation

, Comma

; Semicolon

% Comment

! Exclamation point

‘ Transpose and quote

.’ Nonconjugated transpose

= Assignment

== Equality

< > Relational operators

& Logical and

| Logical or

~ Logical not

xor Logical exclusive or

abs Absolute value (magnitude).

angle Phase angle.

clc Clear Command Window

conv Convolution and polynomial multiplication.

deconv Deconvolution and polynomial division.

freqz Compute the frequency response of digital filters.

impz Compute the impulse response of digital filters.

fir1 Design a window-based finite impulse response filter.

butter Butterworth analog and digital filter design.

cheby1 Chebyshev type I filter design (passband ripple).

cheby2 Chebyshev type II filter design (stopband ripple).

ellip Elliptic (Cauer) filter design.

buttord Calculate the order and cutoff frequency for a

Butterworth filter.

cheb1ord Calculate the order for a Chebyshev type I filter.

cheb2ord Calculate the order for a Chebyshev type II filter.

ellipord Calculate the minimum order for elliptic filters.

besself Bessel analog filter design.

butter Butterworth analog and digital filter design.

cheby1 Chebyshev type I filter design (passband ripple).

cheby2 Chebyshev type II filter design (stopband ripple).

ellip Elliptic (Cauer) filter design.

bilinear Bilinear transformation method for analog-to-digital

filter conversion.

impinvar Impulse invariance method for analog-to-digital filter

conversion.

input Request user input

lp2bp Transform lowpass analog filters to bandpass.

lp2bs Transform lowpass analog filters to bandstop.

lp2hp Transform lowpass analog filters to highpass.

lp2lp Change the cut -off frequency for a lowpass analog filter.

bartlett Compute a Bartlett window.

blackman Compute a Blackman window.

boxcar Compute a rectangular window.

chebwin Compute a Chebyshev window.

hamming Compute a Hamming window.

hann Compute the Hann (Hanning) window.

kaiser Compute a Kaiser window.

triang Compute a triangular window.

fft Compute the one-dimensional fast Fourier transform.

fftshift Rearrange the outputs of the FFT functions.

ifft One-dimensional inverse fast Fourier transform.

ifft2 Two-dimensional inverse fast Fourier transform.

ans The most recent answer

computer Identify the computer on which MATLAB is running

eps Floating-point relative accuracy

i Imaginary unit

Inf Infinity

j Imaginary unit

NaN Not-a-Number

pi Ratio of a circle’s circumference to its diameter,

abs Absolute value and complex magnitude

real Real part of complex number

strcat String concatenation

strcmp Compare strings

det Matrix determinant

norm Vector and matrix norms

null Null space of a matrix

dsp_lab_manual_matlab_ankit

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