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% Chapter 8: Example 8.12 % Impulse Invariance Transformation % Chebyshev-1 Lowpass Filter Design % % Digital Filter Specifications: wp = 0.2*pi;

% Chapter 6: Example 6.7 % Freq. Samp. Form: given frequency samples % M = 32; alpha = (M-1)/2; k = 0:M-1; wk = (2*pi/M)*k; magHk = [1,1,1,0.5,zeros(1,25),0.5,1,1]; k1 = 0:15; k2 = 16:

subplot(1,1,1) n = 0:10; x = (0.9*exp(j*pi/3)).^n; k = -200:200; w = (pi/100)*k; X = x * (exp(-j*pi/100)) .^ (n'*k); magX = abs(X); angX =angle(X); subplot(2,1,1); plot(w/pi,magX);grid axis([-2,

n = -5:10; x = rand(1,length(n)); k = -100:100; w = (pi/100)*k; % frequency between -pi and +pi X = x * (exp(-j*pi/100)).^(n'*k); % DTFT of x % folding property y = fliplr(x); m = -flipl

w = [0:1:500]*pi/500; % [0, pi] axis divided into 501 points. X = exp(j*w) ./ (exp(j*w) - 0.9*ones(1,501)); magX = abs(X); angX = angle(X); subplot(2,1,1); plot(w/pi,magX); grid; axis([0,1,0,10])

b = [0.0181, 0.0543, 0.0543, 0.0181]; a = [1.0000, -1.7600, 1.1829, -0.2781]; m = 0:length(b)-1; l = 0:length(a)-1; K = 500; k = 1:1:K; w = pi*k/K; % [0, pi] axis divided into 501 points. num

x1 = rand(1,11); x2 = rand(1,11); n = 0:10; alpha = 2; beta = 3; k = 0:500; w = (pi/500)*k; X1 = x1 * (exp(-j*pi/500)).^(n'*k); % DTFT of x1 X2 = x2 * (exp(-j*pi/500)).^(n'*k); % DTFT of x2 x =

n = 0:100; x = cos(pi*n/2); k = -100:100; w = (pi/100)*k; % frequency between -pi and +pi X = x * (exp(-j*pi/100)).^(n'*k); % DTFT of x % y = exp(j*pi*n/4).*x; % signal mu

w = [-100:100]*pi/100; % frequency between -pi and +pi N = 5; X1 = sin((w+eps)*N/2)./sin((w+eps)/2); N = 15; X2 = sin((w+eps)*N/2)./sin((w+eps)/2); N = 25; X3 = sin((w+eps)*N/2)./sin((w+eps)/2);

w = [0:1:500]*pi/500; % [0, pi] axis divided into 501 points. X = exp(j*w) ./ (exp(j*w) - 0.5*ones(1,501)); magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X); subplot(2,2,1); plot(