《DSP using MATLAB》 Problem 3.22
代码：
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%% Output Info about this m-file
fprintf(\'\n***********************************************************\n\');
fprintf(\' <DSP using MATLAB> Problem 3.22 \n\n\');
banner();
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%% 1 xa(t)=cos(20πt+θ) through A/D
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Ts = 0.05; % sample interval, 0.05s
Fs = 1/Ts; % Fs=20Hz
%theta = 0;
%theta = pi/6;
%theta = pi/4;
%theta = pi/3;
theta = pi/2;
n1_start = 0; n1_end = 20;
n1 = [n1_start:1:n1_end];
nTs = n1 * Ts; % [0, 1]s
x1 = cos(20*pi*nTs + theta * ones(1,length(n1))); % Digital signal
M = 500;
[X1, w] = dtft1(x1, n1, M);
magX1 = abs(X1); angX1 = angle(X1); realX1 = real(X1); imagX1 = imag(X1);
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%% START X(w)\'s mag ang real imag
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figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 X1, theta/pi = %f\', theta/pi));
set(gcf,\'Color\',\'white\');
subplot(2,1,1); plot(w/pi,magX1); grid on; %axis([-1,1,0,1.05]);
title(\'Magnitude Response\');
xlabel(\'frequency in \pi units\'); ylabel(\'Magnitude |H|\');
subplot(2,1,2); plot(w/pi, angX1/pi); grid on; %axis([-1,1,-1.05,1.05]);
title(\'Phase Response\');
xlabel(\'frequency in \pi units\'); ylabel(\'Radians/\pi\');
figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 X1, theta/pi = %f\', theta/pi));
set(gcf,\'Color\',\'white\');
subplot(2,1,1); plot(w/pi, realX1); grid on;
title(\'Real Part\');
xlabel(\'frequency in \pi units\'); ylabel(\'Real\');
subplot(2,1,2); plot(w/pi, imagX1); grid on;
title(\'Imaginary Part\');
xlabel(\'frequency in \pi units\'); ylabel(\'Imaginary\');
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%% END X\'s mag ang real imag
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figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 xa(n), theta/pi = %f and x1(n)\', theta/pi));
na1 = 0:0.01:1;
xa1 = cos(20 * pi * na1 + theta * ones(1,length(na1)));
set(gcf, \'Color\', \'white\');
plot(1000*na1,xa1); grid on; %axis([0,1,0,1.5]);
title(\'x1(n) and xa(n)\');
xlabel(\'t in msec.\'); ylabel(\'xa(t)\'); hold on;
plot(1000*nTs, x1, \'o\'); hold off;
%% ------------------------------------------------------------
%% xa(t) reconstruction from x1(n)
%% ------------------------------------------------------------
Dt = 0.001; t = 0:Dt:1;
xa = x1 * sinc(Fs*(ones(length(n1),1)*t - nTs\'*ones(1,length(t)))) ;
figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 Reconstructed From x1(n), theta/pi = %f\', theta/pi));
set(gcf,\'Color\',\'white\');
%subplot(2,1,1);
stairs(t*1000,xa,\'r\'); grid on; %axis([0,1,0,1.5]); % Zero-Order-Hold
title(\'Reconstructed Signal from x1(n) using Zero-Order-Hold\');
xlabel(\'t in msec.\'); ylabel(\'xa(t)\'); hold on;
%stem(nTs*1000, x1); gtext(\'ZOH\'); hold off;
plot(nTs*1000, x1, \'o\'); gtext(\'ZOH\'); hold off;
figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 Reconstructed From x1(n), theta/pi = %f\', theta/pi));
set(gcf,\'Color\',\'white\');
%subplot(2,1,2);
plot(t*1000,xa,\'r\'); grid on; %axis([0,1,0,1.5]); % first-Order-Hold
title(\'Reconstructed Signal from x1(n) using First-Order-Hold\');
xlabel(\'t in msec.\'); ylabel(\'xa(t)\'); hold on;
plot(nTs*1000,x1,\'o\'); gtext(\'FOH\'); hold off;
xa = spline(nTs, x1, t);
figure(\'NumberTitle\', \'off\', \'Name\', sprintf(\'Problem 3.22 Reconstructed From x1(n), theta/pi = %f\', theta/pi));
set(gcf,\'Color\',\'white\');
%subplot(2,1,1);
plot(1000*t, xa,\'r\');
xlabel(\'t in ms units\'); ylabel(\'x\');
title(sprintf(\'Reconstructed Signal from x1(n) using Spline function\')); grid on; hold on;
plot(1000*nTs, x1,\'o\'); gtext(\'spline\');
运行结果：
这里只看初相位为0的情况，原始模拟信号和采样信号（样点值圆圈标示）：
采样信号的谱，模拟角频率20π对应的数字角频率为π，如下图所示：
用采样信号重建原来模拟信号：
sinc方法，stairs函数画图
sinc方法，plot函数画图：
cubic方法
其他初相位的情况，这里不上图了。