《DSP using MATLAB》示例Example 8.14
%% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Exameple 8.14 \n\n'); time_stamp = datestr(now, 31); [wkd1, wkd2] = weekday(today, 'long'); fprintf(' Now is %20s, and it is %8s \n\n', time_stamp, wkd2); %% ------------------------------------------------------------------------ % Digital Filter Specifications: wp = 0.2*pi; % digital passband freq in rad ws = 0.3*pi; % digital stopband freq in rad Rp = 1; % passband ripple in dB As = 15; % stopband attenuation in dB % Analog prototype specifications: Inverse Mapping for frequencies T = 1; % set T = 1 OmegaP = wp/T; % prototype passband freq OmegaS = ws/T; % prototype stopband freq % Analog Elliptic Prototype Filter Calculation: [cs, ds] = afd_elip(OmegaP, OmegaS, Rp, As); % Impulse Invariance Transformation: [b, a] = imp_invr(cs, ds, T); [C, B, A] = dir2par(b, a) % Calculation of Frequency Response: [db, mag, pha, grd, ww] = freqz_m(b, a); %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- figure('NumberTitle', 'off', 'Name', 'Exameple 8.14') set(gcf,'Color','white'); M = 1; % Omega max subplot(2,2,1); plot(ww/pi, mag); axis([0, M, 0, 1.2]); grid on; xlabel(' frequency in \pi units'); ylabel('|H|'); title('Magnitude Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.1778, 0.8913, 1]); subplot(2,2,2); plot(ww/pi, pha/pi); axis([0, M, -1.1, 1.1]); grid on; xlabel('frequency in \pi nuits'); ylabel('radians in \pi units'); title('Phase Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]); subplot(2,2,3); plot(ww/pi, db); axis([0, M, -30, 10]); grid on; xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude in dB '); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-30, -15, -1, 0]); subplot(2,2,4); plot(ww/pi, grd); axis([0, M, 0, 20]); grid on; xlabel('frequency in \pi units'); ylabel('Samples'); title('Group Delay'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0:5:20]);
运行结果:
从图上看出,脉冲不变设计方法又失败了。
脉冲不变方法的优点是稳定的设计,频率Ω和ω是线性相关的。但是缺点是模拟频率响应中有一些假频,某些情况下假频是无法容忍的。
结论:该设计方法仅当模拟滤波器是带限到低通或带通的情况(阻带中没有振荡)。
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