《DSP using MATLAB》示例Example 9.7

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Exameple 9.7 \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);
%% ------------------------------------------------------------------------

I = 4; L = 5;
%n = 0:2048; k1 = 256; 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 9.7');
set(gcf,'Color','white'); 

TF = 10;
% (a) Full singal bandwidth: alpha = 1
I
L
alpha = 1; h = intfilt(I, L, alpha);
fprintf('\n  The Length of filter is %d \n', length(h) );

[Hr, w, a, LL] = 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, 1);
plot(w/pi, Hr, 'g', 'linewidth', 1.0); axis([0, 1, -1, 5]); grid on;
xlabel('frequency in \pi units'); ylabel('Amplitude');
title('Amplitude Response:alpha = 1 ', 'fontsize', TF);
set(gca, 'xtick', [0, 1/I, 1]);
set(gca, 'ytick', [0, I]);

subplot(2, 2, 3);
plot(w/pi, Hdb, 'm', 'linewidth', 1.0); axis([0, 1, -50, 10]); grid on;
xlabel('frequency in \pi units', 'fontsize', 10); ylabel('Decibels');
title(' Log-mag Response : alpha = 1 ', 'fontsize', TF);
set(gca, 'xtick', [0, 1/I, 1]);
set(gca, 'ytick', [-50,  round(min_attn), 0]);

% (b) Partial signal bandwidth: alpha = 0.75
I
L
alpha = 0.75; h = intfilt(I, L, alpha);

fprintf('\n  The Length of filter is %d \n', length(h) );

[Hr, w, a, LL] = Hr_Type1(h); Hr_min = max(Hr(end/2:end)); 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, 'g', 'linewidth', 1.0); axis([0, 1, -1, 5]); grid on;
xlabel('frequency in \pi units '); ylabel('Amplitude');
title('Amplitude Response : alpha = 0.75 ', 'fontsize', TF);
set(gca, 'xtick', [0, 1/I, 1]);
set(gca, 'ytick', [ 0, I]);

subplot(2, 2, 4); plot(w/pi, Hdb, 'm', 'linewidth', 1.0); axis([0, 1, -50, 10]); grid on;
xlabel('frequency in \pi units'); ylabel('Decibels');
title('Log-mag Response: alpha = 0.75', 'fontsize', TF);
set(gca, 'xtick', [0, 1/I, 1]);
set(gca, 'ytick', [-50, round(min_attn), 0]);

　　运行结果：

可见，两种α情况下，intfilt函数得到的脉冲响应h长度为2×I×L-1=2×4×5-1=39，即数组h(n)有39个元素。

对于全频带alpha=1的情况，滤波器在通带和阻带都有更多的振荡，最小的阻带衰减是22dB。这是由过渡带很窄造成的。
当alpha=0.75时，滤波器特征是很宽容的，因此它的响应最小阻带衰减34dB。

另外注意到我们没有完全控制其他设计参数。这些细节本节随后会有更详细的讨论。