《DSP using MATLAB》示例 Example 9.4

Posted 2020-09-19 沧海一粟

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(\'\\n***********************************************************\\n\');
fprintf(\'        <DSP using MATLAB> Exameple 9.4 \\n\\n\');

time_stamp = datestr(now, 31);
[wkd1, wkd2] = weekday(today, \'long\');
fprintf(\'      Now is %20s, and it is %7s  \\n\\n\', time_stamp, wkd2);
%% ------------------------------------------------------------------------

n = 0:256; k1 = 64; k2 = k1+32; m = 0:(k2-k1);


%% -----------------------------------------------------------------
%%                             Plot
%% -----------------------------------------------------------------  
Hf1 = figure(\'units\', \'inches\', \'position\', [1, 1, 8, 6], ...
	\'paperunits\', \'inches\', \'paperposition\', [0, 0, 6, 4], ...
	\'NumberTitle\', \'off\', \'Name\', \'Exameple 9.4\');
set(gcf,\'Color\',\'white\'); 

TF = 10;
% (a) Original signal
x = cos(pi*n); subplot(2, 2, 1); 
Ha = stem(m, x(m+k1+1), \'g\', \'filled\'); axis([-1, 33, -1.1, 1.1]); grid on;
set(Ha, \'markersize\', 2); xlabel(\'n\'); ylabel(\'Amplitude\'); 
title(\'Original Sequence x(n)\', \'fontsize\', TF);
set(gca, \'xtick\', [0, 16, 32]); 
set(gca, \'ytick\', [-1, 0, 1]);

% (b) Interpolation by D = 2
I = 2; y = interp(x, I); subplot(2, 2, 2); 
Hb = stem(m, y(m+k1*I+1), \'c\', \'filled\'); axis([-1, 33, -1.1, 1.1]); grid on;
set(Hb, \'markersize\', 2); xlabel(\'n\'); ylabel(\'Amplitude\');
title(\'Interpolated by I = 2\', \'fontsize\', TF);
set(gca, \'xtick\', [0, 16, 32]); 
set(gca, \'ytick\', [-1, 0, 1]);

% (c) Interpolation by I = 4
I = 4; y = interp(x, I); subplot(2, 2, 3); 
Hc = stem(m, y(m+k1*I+1), \'r\', \'filled\'); axis([-1, 33, -1.1, 1.1]); grid on;
set(Hc, \'markersize\', 2); xlabel(\'n\'); ylabel(\'Amplitude\');
title(\'Interpolated by I = 4\', \'fontsize\', TF);
set(gca, \'xtick\', [0, 16, 32]); 
set(gca, \'ytick\', [-1, 0, 1]);

% (d) Interpolation by I = 8
I = 8; y = interp(x, I); subplot(2, 2, 4); 
Hd = stem(m, y(m+k1*I+1), \'m\', \'filled\'); axis([-1, 33, -1.1, 1.1]); grid on;
set(Hd, \'markersize\', 2); xlabel(\'n\'); ylabel(\'Amplitude\');
title(\'Interpolated by I = 8\', \'fontsize\', TF);
set(gca, \'xtick\', [0, 16, 32]); 
set(gca, \'ytick\', [-1, 0, 1]);

　　运行结果：

      从图看，I的所有三个数值下的插值序列是合适的，在更高的采样率上展示了原始正弦信号x(n)。I=8的例子里，

插值序列从形状上看不像是精确的正弦信号。这可能是由于低通滤波器和理想低通滤波器有差距而造成的。