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《DSP using MATLAB》示例Example 8.21
%% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf(‘\n***********************************************************\n‘); fprintf(‘ <DSP using MATLAB> Exameple 8.21 \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 = (2/T)*tan(wp/2); % Prewarp(Cutoff) prototype passband freq OmegaS = (2/T)*tan(ws/2); % Prewarp(cutoff) prototype stopband freq % Analog Prototype Order Calculations: N = ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(OmegaP/OmegaS))); fprintf(‘\n\n ********** Butterworth Filter Order = %3.0f \n‘, N) OmegaC = OmegaP/((10^(Rp/10)-1)^(1/(2*N))); % Analog BW prototype cutoff freq wn = 2*atan((OmegaC*T)/2); % Digital BW cutoff freq % Digital Butterworth Filter Design: wn = wn/pi; % Digital Butterworth cutoff freq in pi units [b, a] = butter(N, wn); [C, B, A] = dir2cas(b, a) % Calculation of Frequency Response: [db, mag, pha, grd, ww] = freqz_m(b, a); %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Exameple 8.21‘) 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, 15]); 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‘, [0:5:15]);
运行结果:
《DSP using MATLAB》示例Example 8.21
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