代码: function [X1k, X2k] = real2dft(x1, x2, N) %% --------------------------------------------------------------------- %% DFT of two Real-Valued N-Point sequence x1(n) and x2(n) %% ---------------------------------------------------------------------…

先求模拟信号经过采样后,对应的数字角频率: 明显看出,第3种采样出现假频了.DTFT是以2π为周期的,所以假频出现在10π-2kπ=0处. 代码: %% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n********************************************************…

代码: %% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Problem 2.19 \n\n'); banner();…

代码: %% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Problem 8.19 \n\n'); banner();…

代码: % Analog Signal Dt = 0.00005; t = -0.005:Dt:0.005; xa = exp(-1000*abs(t)); % Discrete-time Signal Ts = 0.0002; n = -25:1:25; x = exp(-1000*abs(n*Ts)); % Discrete-time Fourier Transform %Wmax = 2*pi*2000; K = 500; k = 0:1:K; w = pi*k/K; % index ar…

代码: % Discrete-time Signal x1(n) % Ts = 0.0002; n = -25:1:25; nTs = n*Ts; Fs = 1/Ts; x = exp(-1000*abs(nTs)); Ts = 0.001; n = -5:1:5; nTs = n*Ts; Fs = 1/Ts; x = exp(-1000*abs(nTs)); % Analog Signal Dt = 0.00005; t = -0.005:Dt:0.005; xa = x * sinc(Fs*…

代码: % Analog Signal Dt = 0.00005; t = -0.005:Dt:0.005; xa = exp(-1000*abs(t)); % Continuous-time Fourier Transform Wmax = 2*pi*2000; K = 500; k = 0:1:K; % index array k for frequencies W = k*Wmax/K; % freqency between 0 and +pi, [0,pi] axis divided i…

代码: % Discrete-time Signal x1(n) : Ts = 0.0002 Ts = 0.0002; n = -25:1:25; nTs = n*Ts; x1 = exp(-1000*abs(nTs)); figure('NumberTitle', 'off', 'Name', 'Example3.23 Reconstructed From x1(n)'); set(gcf,'Color','white'); subplot(2,1,1); stairs(nTs*1000,x1…

代码: % Discrete-time Signal x2(n) Ts = 0.001; n = -5:1:5; nTs = n*Ts; Fs = 1/Ts; x = exp(-1000*abs(nTs)); % Analog Signal Dt = 0.00005; t = -0.005:Dt:0.005; xa = x * sinc(Fs*(ones(length(n),1)*t - nTs'*ones(1,length(t)))) ; % check error = max(abs(xa…

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代码: b = [0.0181, 0.0543, 0.0543, 0.0181]; % filter coefficient array b a = [1.0000, -1.7600, 1.1829, -0.2781]; % filter coefficient array a m = 0:length(b)-1; l = 0:length(a)-1; % index arrays m and l K = 500; k = 0:1:K; % index array k for frequenci…

上代码: subplot(1,1,1); b = 1; a = [1, -0.8]; n = [0:100]; x = cos(0.05*pi*n); y = filter(b,a,x); figure('NumberTitle', 'off', 'Name', 'Input and Output sequence'); set(gcf,'Color','white'); subplot(2,1,1); stem(n,x); title('Input sequence'); xlabel('n'…

上代码: w = [0:1:500]*pi/500; % freqency between 0 and +pi, [0,pi] axis divided into 501 points. H = exp(j*w) ./ (exp(j*w) - 0.9 * ones(1,501)); magH = abs(H); angH = angle(H); realH = real(H); imagH = imag(H); %% ---------------------------------------…

用到的性质 代码: n = -5:10; x = sin(pi*n/2); k = -100:100; w = (pi/100)*k; % freqency between -pi and +pi , [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); % DTFT of x % signal decomposition [xe,xo,m] = evenodd(x,n); % even and odd…

用到的性质 上代码: n = -5:10; x = rand(1,length(n)); k = -100:100; w = (pi/100)*k; % freqency between -pi and +pi , [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); % DTFT of x % folding property y = fliplr(x); m = -fliplr(n); % signa…

用到的性质 上代码: n = -5:10; x = rand(1,length(n)) + j * rand(1,length(n)); k = -100:100; w = (pi/100)*k; % freqency between -pi and +pi , [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); % DTFT of x % conjugation property y = conj(x…

用到的性质 上代码: n = 0:100; x = cos(pi*n/2); k = -100:100; w = (pi/100)*k; % freqency between -pi and +pi , [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); % DTFT of x % signal multiplied y = exp(j*pi*n/4) .* x; % signal multiplied…

代码: x = rand(1,11); n = 0:10; k = 0:500; w = (pi/500)*k; % [0,pi] axis divided into 501 points. 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 of y = x(n-2)…

上代码: x1 = rand(1,11); x2 = rand(1,11); n = 0:10; alpha = 2; beta = 3; k = 0:500; w = (pi/500)*k; % [0,pi] axis divided into 501 points. X1 = x1 * (exp(-j*pi/500)) .^ (n'*k); % DTFT of x1 X2 = x2 * (exp(-j*pi/500)) .^ (n'*k); % DTFT of x2 x = alpha *…

代码: n = [-5:5]; x = (-0.9).^n; % x(n) = k = -200:200; w = (pi/100)*k; % [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X); set(gcf,'Color','white'); subplot(2,2,1…

代码: n = [0:10]; x = (0.9*exp(j*pi/3)).^n; % x(n) = k = -200:200; w = (pi/100)*k; % [0,pi] axis divided into 101 points. X = x * (exp(-j*pi/100)) .^ (n'*k); magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X); set(gcf,'Color','white'); su…

代码: n = [-1:3]; x = [1:5]; % x(n) = {1,2,3,4,5} % * % k = 0:500; w = (pi/500)*k; % [0,pi] axis divided into 501 points. X = x * (exp(-j*pi/500)) .^ (n'*k); magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X); set(gcf,'Color','white'); su…

上代码: 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); set(gcf,'Color','white'); subplot(2,2,1); plot(w/pi,magX); grid on; titl…

代码: b = [1]; a = [1, -0.9]; n = [-5:50]; h = impz(b,a,n); set(gcf,'Color','white'); %subplot(2,1,1); stem(n,h); title('Impulse Response'); xlabel('n'); ylabel('h(n)'); grid on; x = stepseq(0, -5, 50) - stepseq(10, -5, 50) y = filter(b, a, x); figure;…

上代码: b = [1]; a = [1, -1, 0.9]; n = [-20:120]; h = impz(b,a,n); set(gcf,'Color','white'); %subplot(2,1,1); stem(n,h); title('Impulse Response'); xlabel('n'); ylabel('h(n)'); grid on; x = stepseq(0,-20, 120); s = filter(b,a,x); figure; set(gcf,'Color'…

上代码 % noise sequence 1 x = [3, 11, 7, 0, -1, 4, 2]; nx = [-3:3]; % given signal x(n) [y,ny] = sigshift(x,nx,2); % obtain x(n-2) set(gcf,'Color','white') subplot(2,1,1);stem(nx,x); title('sequence x(n)'); xlabel('n');ylabel('x(n)'); grid on subplot(2,…

n = [0:10]; x = stepseq(0,0,10) - stepseq(10,0,10); [xe,xo,m] = evenodd(x,n); set(gcf,'Color',[1,1,1]) % 改变坐标外围背景颜色 stem(n,x); title('Rectangular Pulse'); xlabel('n'); ylabel('x(n)') ; axis([-10,10,0,1.2]) grid on figure set(gcf,'Color',[1,1,1]) stem…

n = [-10:1:10]; alpha = -0.1+0.3j; % x = exp(alpha*n); % subplot(2,1,1); set(gcf,'Color',[1,1,1]) % 改变坐标外围背景颜色 stem(n,real(x)); title('real part'); xlabel('n'); grid on figure set(gcf,'Color','white') % 新生成一张图 stem(n,imag(x)); title('imaginary part')…

a. n = -2:10; x = [1:7,6:-1:1]; % generate x(n) [x11,n11] = sigshift(x,n,5); [x12,n12] = sigshift(x,n,-4); [x1,n1] = sigadd(2 * x11, n11, -3 * x12, n12); set(gcf,'Color',[1,1,1]) % 改变坐标外围背景颜色 stem(n,x); title('Sequence x(n)') xlabel('n');ylabel('x(n)…

代码: %% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Exameple 8.19 \n\n'); time_stam…