《DSP using MATLAB》示例9.2

Posted 2020-09-19 沧海一粟

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(\'\\n***********************************************************\\n\');
fprintf(\'        <DSP using MATLAB> Exameple 9.2 \\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 = 0:2048; k1 = 256; k2 = k1+32; m = 0:(k2-k1);


%% -----------------------------------------------------------------
%%                             Plot
%% -----------------------------------------------------------------  
Hf1 = figure(\'units\', \'inches\', \'position\', [1, 1, 9, 7], ...
	\'paperunits\', \'inches\', \'paperposition\', [0, 0, 6, 4], ...
	\'NumberTitle\', \'off\', \'Name\', \'Exameple 9.2\');
set(gcf,\'Color\',\'white\'); 

TF = 10;
% (a) Original signal
x = cos(0.125*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) Decimation by D = 2
D = 2; y = decimate(x, D); subplot(2, 2, 2); 
Hb = stem(m, y(m+k1/D+1), \'c\', \'filled\'); axis([-1, 33, -1.1, 1.1]); grid on;
set(Hb, \'markersize\', 2); xlabel(\'n\'); ylabel(\'Amplitude\');
title(\'Decimated by D = 2\', \'fontsize\', TF);
set(gca, \'xtick\', [0, 16, 32]); 
set(gca, \'ytick\', [-1, 0, 1]);

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

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

　　运行结果：

        我们将画出信号的中间段，来避免默认低通滤波器的末端效应。默认低通采样8阶切比雪夫I型，截止频率0.8π/D(本例子来说分别是0.4π、0.2π和0.1π三个截止频率。)

从图中看出，按D=2和D=4减采样序列是正确的，在低采样率情况下展示了原始正弦序列x(n)；但是，D=8的序列几乎为零，原因就是首先对输入序列进行低通，然后再

减采样。MATLAB中decimat函数使用低通的截止频率为0.1π，原始信号0.125π几乎消减没了。