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n = -5:10; x = sin(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 % signal decomposition [xe,xo,m] = evenodd(x,n);

% Chapter 3: Example 3.4: % DTFT of finite duration seq using mat-vec operation % n = -1:3; x = 1:5; % sequence x(n) k = 0:500; w = (pi/500)*k; % [0, pi] axis divided in

subplot(1,1,1) n = -5:5; x = (-0.9).^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([-2,2,0,15]) x

x = rand(1,11); n = 0:10; k = 0:500; w = (pi/500)*k; X = x * (exp(-j*pi/500)).^(n'*k); % DTFT of x % signal shifted by two samples y = x; m = n+2; Y = y * (exp(-j*pi/500)).^(m'*k); % DTFT o

n = -5:10; x = rand(1,length(n)) + j*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 % conjugation property

% Chapter 05: Example 05.08: HiRes Spectrum % % High resolution spectrum based on 100 samples of the signal x(n) subplot(1,1,1) n=[0:1:99]; x=cos(0.48*pi*n)+cos(0.52*pi*n); subplot(2,1,1);stem(n

% Chapter 05: Example 05.06: Simple DFT Example % x = [1,1,1,1]; subplot(1,1,1); % % a) DTFT w = [0:1:500]*2*pi/500; [H] = freqz(x,1,w); magH = abs(H); phaH = angle(H); phaH(126)=-47.5841*pi/1

% Chapter 05: Example 05.07: Zero-padding Example % subplot(1,1,1); x = [1,1,1,1]; % % a) DTFT w = [0:1:500]*2*pi/500; [H] = freqz(x,1,w); magH = abs(H); phaH = angle(H); phaH(126)=-47.5841*pi

% Chapter 05: Example 05.08 % High density vs HiRes Spectrum % % signal x(n) subplot(1,1,1); n = [0:1:99]; x = cos(0.48*pi*n)+cos(0.52*pi*n); % % Spectrum based on the first 10 samp

采用频率取样设计法设计FIR数字低通滤波器，满足以下指标 ， ， a．取N = 20，过渡带没有样本。 b．取N = 40，过渡带有一个样本，T = 0.39。 c．取N = 60，过渡带有两个样本，T1 = 0.5925，T2 = 0.1099 N=20;alpha=(N-1)/2;l=0:N-1;wl=(2*pi/N)*l; Hrs=[1,1,1,zer