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DATA=0;
while DATA==0
Nb = 5; %
N = 0; %
T = 0.0115; %
a = -0.825; %
C = 1; %
w0 = 0.523; %
m = 5; %
U = 5; %
n0 = 3; %
n_imp = 5; %
B = [1.5, 5.7, 2.2] ; %
w = [0.785, 0.3925, 0.196]; %
A = [1.5, 0.7, 1.4] ; %
Mean = 3; %
Var = 5;
disp('% ')
disp('% 1')
disp('% 0 ')
DATA = input('--> ');
end
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .1. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
n = 0:(N-1); nT = T.*n; %
u0 = [1 zeros(1,(N-1))]; %
figure('Name','Digital Unit Impulse, Unit Step, and Discrete Exponent','NumberTitle', 'off')
subplot(3,2,1),stem(nT,u0,'Linewidth',2), grid
title('Digital Unit Impulse u0(nT)')
subplot(3,2,2),stem(n,u0,'Linewidth',2), grid
title('Digital Unit Impulse u0(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .2. ');
disp('%')
disp('%')
disp('% <ENTER>')
pause
u1 = [1 ones(1,(N-1))]; %
subplot(3,2,3),stem(nT,u1,'Linewidth',2), grid
title('Digital Unit Step u1(nT)'),
subplot(3,2,4),stem(n,u1,'Linewidth',2), grid
title('Digital Unit Step u1(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .3. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
x1 = a.^n; %
subplot(3,2,5),stem(nT,x1,'Linewidth',2), xlabel('nT'), grid
title('Discrete Exponent x1(nT)')
subplot(3,2,6),stem(n, x1,'Linewidth',2), xlabel('n'), grid
title('Discrete Exponent x1(n)'),
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .4. ')
disp('%')
disp('%')
disp('% ')
disp('% <ENTER>')
pause
x2 = C.*exp(j*w0.*n); %
figure('Name','Discrete Harmonic Signal','NumberTitle', 'off')
subplot(2,1,1),stem(n,real(x2) ,'Linewidth',2), grid
title('Discrete Harmonic Signal: REAL [x2(n)]')
subplot(2,1,2),stem(n,imag(x2) ,'Linewidth',2), xlabel('n'), grid
title(' Discrete Harmonic Signal: IMAG [x2(n)]')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .5. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
u0_m = [zeros(1,m) u0(1:(N-m))]; %
u1_m = [zeros(1,m) u1(1:(N-m))]; %
x1_m = [zeros(1,m) x1(1:(N-m))]; %
figure('Name','Delayed Discrete Signals','NumberTitle', 'off')
subplot(3,1,1),stem(n,u0_m,'Linewidth',2), grid
title ('Delayed Digital Unit Impulse u0(n-m)')
subplot(3,1,2),stem(n,u1_m,'Linewidth',2), grid
title ('Delayed Digital Unit Step u1(n-m)')
subplot(3,1,3),stem(n,x1_m,'Linewidth',2),xlabel('n'), grid
title ('Delayed Discrete Exponent x1(n-m)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .6. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
x3_1 = U*rectpuls(n-n0,2*n_imp); x3_1(1:n0) = 0; % rectpuls
x3_2 = [zeros(1,n0) U.*u1((n0+1):(n0+n_imp))...
zeros(1,N-(n0+n_imp))]; %
figure('Name','Discrete Rectangular and Triangular Impulses','NumberTitle', 'off')
subplot(3,1,1),stem(n,x3_1,'Linewidth',2), grid
title('Discrete Rectangular Impulse x3 1(n)')
subplot(3,1,2),stem(n,x3_2,'Linewidth',2), grid
title('Discrete Rectangular Impulse x3 2 (n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .7. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
x4 = conv(x3_1,x3_1); %
L = 2*N-1; %
n = 0:(L-1); %
subplot(3,1,3),stem(n,x4,'Linewidth',2), xlabel('n'), grid
title('Discrete Triangular Impulse x4(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .8. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
n = 0:(5*N-1); %
xi = repmat(B,length(n),1).*sin(n'*w); %
ai = repmat(A,length(n),1); %
x5 = sum((ai.* xi)'); %
figure('Name','Discrete Harmonic Signals and their Linear Combination','NumberTitle', 'off')
subplot(4,1,1),stem(n, xi(:,1),'Linewidth',2), grid
title('First Discrete Harmonic Signal')
subplot(4,1,2),stem(n, xi(:,2),'Linewidth',2), grid
title('Second Discrete Harmonic Signal')
subplot(4,1,3),stem(n, xi(:,3),'Linewidth',2), grid
title('Third Discrete Harmonic Signal')
subplot(4,1,4),stem(n,x5,'Linewidth',2), xlabel('n'), grid
title('Linear Combination x5(n)')
disp('%')
disp('%')
disp('% , x5 <ENTER>')
pause
mean_x5 = mean(x5); %
E = sum(x5.^2); %
P = sum(x5.^2)/length(x5); %
disp('%')
disp('%')
disp([' mean_x5 = ' num2str(mean_x5) ' E = ' num2str(E) ' P = ' num2str(P)])
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .9. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
n = 0:(N-1); %
x = C.*sin(w0.*n); %
x6 = x.*(abs(a).^n); %
figure('Name','Harmonic Signal with Exponential Envelope. Periodic Sequence of Rectangular Impulses','NumberTitle', 'off')
subplot(2,1,1),stem(n,x6,'Linewidth',2), grid
title('Harmonic Signal with Exponential Envelope x6(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .10. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
xp = [U.*u1(1:n_imp) zeros(1,n_imp)]; %
p = 5; %
x7 = repmat(xp,1,p); %
n = 0:(length(x7)-1); %
subplot(2,1,2), stem(n,x7,'Linewidth',2), xlabel('n'), grid
title('Periodic Sequence of Rectangular Impulses x7(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .11. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
r_uniform = rand(1,10000); %
mean_uniform = mean(r_uniform); % .
var_uniform = var(r_uniform); %
disp('%')
disp('%')
disp([' mean_uniform = ' num2str(mean_uniform) ' var_uniform = ' num2str(var_uniform)])
disp('%')
disp('%')
disp('% <ENTER>')
pause
r_r_uniform = (1/length(r_uniform)).*xcov(r_uniform); %
m = -(length(r_uniform)-1):(length(r_uniform)-1); %
figure('Name','Autocovariance Function of Uniform White Noise','NumberTitle', 'off')
stem(m,r_r_uniform,'Linewidth',2), xlabel('m'), grid
title('Autocovariance Function of Uniform White Noise')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .12. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
r_norm = randn(1,10000); %
mean_norm = mean(r_norm); % .
var_norm = var(r_norm); %
disp('%')
disp('%')
disp([' mean_norm = ' num2str(mean_norm) ' var_norm = ' num2str(var_norm)])
disp('%')
disp('%')
disp('% <ENTER>')
pause
R_r_norm = (1/length(r_norm)).*xcorr(r_norm); %
m = -(length(r_norm)-1):(length(r_norm)-1); %
figure('Name','ACF of White Gaussian Noise','NumberTitle', 'off')
stem(m,R_r_norm,'Linewidth',2), xlabel('m'), grid
title('ACF of White Gaussian Noise')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .13. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
n = 0:(N-1); %
x8 = x+randn(1,N); %
figure('Name','Mixture of Harmonic Signal and White Gaussian Noise and ACF','NumberTitle', 'off')
subplot(2,1,1),stem(n,x8,'Linewidth',2),xlabel('n'), grid
title('Mixture of Harmonic Signal and White Gaussian Noise x8(n)')
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .14. ')
disp('%')
disp('%')
disp('% <ENTER>')
pause
R = (1/N).*xcorr(x8); %
m = -(N-1):(N-1); %
subplot(2,1,2),stem((m),R,'Linewidth',2),xlabel('m'), grid
title('ACF R(m)')
disp('%')
disp('%')
disp('% R(N) <ENTER>')
pause
disp('%')
disp('%')
disp([' var_x8 = ' num2str(var(x8))])
disp([' R(N) = ' num2str(R(N))])
disp('%')
disp('%')
disp('% <ENTER>')
pause
disp('%')
disp('%')
disp('% .15. ')
r_normMean = randn(1,10000)+Mean; %
r_normVar = sqrt(Var).*randn(1,10000); %
r_normMeanVar = sqrt(Var).*randn(1,10000)+ Mean; %
MAX = max([r_norm r_normMean r_normVar r_normMeanVar]);
%
disp('%')
disp('%')
disp('% <ENTER>')
pause
figure('Name','White Gaussian Noises with different statistics','NumberTitle', 'off')
subplot(4,1,1), plot(r_norm), grid, ylim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_norm)),' Variance = ',num2str(var(r_norm))]))
subplot(4,1,2), plot(r_normMean), grid, ylim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normMean)),' Variance = ',num2str(var(r_normMean))]))
subplot(4,1,3), plot(r_normVar), grid, ylim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normVar)),' Variance = ',num2str(var(r_normVar))]))
subplot(4,1,4), plot(r_normMeanVar), xlabel('n'), grid, ylim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normMeanVar)),' Variance = ',num2str(var(r_normMeanVar))]))
disp('%')
disp('%')
disp('% <ENTER>')
pause
figure('Name','Histograms with different statistics','NumberTitle', 'off')
subplot(4,1,1), hist(r_norm), grid, xlim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_norm)),' Variance = ',num2str(var(r_norm))]))
subplot(4,1,2), hist(r_normMean), grid, xlim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normMean)),' Variance = ',num2str(var(r_normMean))]))
subplot(4,1,3), hist(r_normVar), grid, xlim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normVar)),' Variance = ',num2str(var(r_normVar))]))
subplot(4,1,4),hist(r_normMeanVar), grid, xlim([-MAX MAX])
title(strcat([' Mean value = ',num2str(mean(r_normMeanVar)),' Variance = ',num2str(var(r_normMeanVar))]))
disp('%')
disp('%')
disp('% ')