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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('% ')