《DSP using MATLAB》示例 Example 9.14

Posted 2020-09-20 沧海一粟

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(\'\\n***********************************************************\\n\');
fprintf(\'        <DSP using MATLAB> Exameple 9.14 \\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);
%% ------------------------------------------------------------------------

% Given Parameters:

D = 2; Rp = 0.1; As = 50; wxp = pi/8; wxs = pi/D; wp = wxp; ws = (2*pi/D)-wxs; 

% Filter Design:
[delta1, delta2] = db2delta(Rp, As); 

[N, F, A, weights] = firpmord([wp, ws]/pi, [1, 0], [delta1, delta2], 2); N = ceil(N/2)*2;
h = firpm(N, F, A, weights); 
delay = N/2;                        % delay imparted by the filter  


%% -----------------------------------------------------------------
%%                             Plot
%% -----------------------------------------------------------------  

% Input signal x(n) = cos(2*pi*n/16)
n = [0:256]; x = cos(pi*n/8);
n1 = n(1:33); x1 = x(33:65);            % for plotting purposes

Hf1 = figure(\'units\', \'inches\', \'position\', [1, 1, 8, 6], ...
	\'paperunits\', \'inches\', \'paperposition\', [0, 0, 6, 4], ...
	\'NumberTitle\', \'off\', \'Name\', \'Exameple 9.14\');
set(gcf,\'Color\',\'white\'); 

TF = 10;

subplot(2, 2, 1); 
Hs1 = stem(n1, x1, \'filled\'); set(Hs1, \'markersize\', 2, \'color\', \'g\');
axis([-2, 34, -1.2, 1.2]); grid on;
xlabel(\'n\', \'vertical\', \'middle\'); ylabel(\'Amplitude\', \'vertical\', \'middle\'); 
title(\'Input Singal: x(n) = cos(\\pin/8) \', \'fontsize\', TF, \'vertical\', \'baseline\');
set(gca, \'xtick\', [0:8:32]); 
set(gca, \'ytick\', [-1, 0, 1]);

% Decimation of x(n): D = 2
y = upfirdn(x, h, 1, D);
m = delay+1:1:128/D+delay+1; y1 = y(m); m = 0:16; y1 = y1(14:30);

subplot(2, 2, 3); 
Hs2 = stem(m, y1, \'filled\'); set(Hs2, \'markersize\', 2, \'color\', \'m\');
axis([-1, 17, -1.2, 1.2]); grid on;
xlabel(\'m\', \'vertical\', \'middle\'); ylabel(\'Amplitude\', \'vertical\', \'middle\'); 
title(\'Output Singal: y(n): D=2\', \'fontsize\', TF, \'vertical\', \'baseline\');
set(gca, \'xtickmode\', \'manual\', \'xtick\', [0:8:32]/D); 
set(gca, \'ytickmode\', \'manual\', \'ytick\', [-1, 0, 1]);

% Filter Design Plots
[Hr, w, a, L] = Hr_Type1(h); Hr_min = min(Hr); w_min = find(Hr == Hr_min);
H = abs(freqz(h, 1, w)); Hdb = 20*log10(H/max(H)); min_attn = Hdb(w_min);
subplot(2, 2, 2); 
plot(w/pi, Hr, \'m\', \'linewidth\', 1.0); axis([0, 1, -0.1, 1.1]); grid on;
xlabel(\'Frequency in \\pi units\', \'fontsize\', TF, \'vertical\', \'middle\');
ylabel(\'Amplitude\', \'vertical\', \'cap\');
title(\'Amplitude Response\', \'fontsize\', TF, \'vertical\', \'baseline\');
set(gca, \'xtick\', [0, wp/pi, ws/pi, 1], \'ytick\', [0, 1]);


subplot(2, 2, 4); 
plot(w/pi, Hdb, \'m\', \'linewidth\', 1.0); axis([0, 1, -60, 10]); grid on;
xlabel(\'Frequency in \\pi units\', \'fontsize\', TF, \'vertical\', \'middle\');
ylabel(\'Decibels\', \'vertical\', \'cap\');
title(\'Log-magnitude Response\', \'fontsize\', TF, \'vertical\', \'baseline\');
set(gca, \'xtick\', [0, wp/pi, ws/pi, 1], \'ytick\', [-60, round(min_attn), 0]);

　　运行结果：

     设计的滤波器达到51dB的衰减，并且减采样的信号是正确的。