代码:
%% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Problem 8.35 \n\n'); banner(); %% ------------------------------------------------------------------------ % Digital Highpass Filter Specifications: wphp = 0.6*pi; % digital passband freq in rad wshp = 0.4*pi; % digital stopband freq in rad Rp = 0.5; % passband ripple in dB As = 60; % stopband attenuation in dB Ripple = 10 ^ (-Rp/20) % passband ripple in absolute Attn = 10 ^ (-As/20) % stopband attenuation in absolute fprintf('\n*******Digital Highpass, Coefficients of DIRECT-form***********\n'); %[bhp, ahp] = butthpf(wphp, wshp, Rp, As) [bhp, ahp] = cheb1hpf(wphp, wshp, Rp, As) %[bhp, ahp] = cheb2hpf(wphp, wshp, Rp, As) %[bhp, ahp] = eliphpf(wphp, wshp, Rp, As) [C, B, A] = dir2cas(bhp, ahp); % Calculation of Frequency Response: %[dblp, maglp, phalp, grdlp, wwlp] = freqz_m(blp, alp); [dbhp, maghp, phahp, grdhp, wwhp] = freqz_m(bhp, ahp); % --------------------------------------------------------------- % find Actual Passband Ripple and Min Stopband attenuation % --------------------------------------------------------------- delta_w = 2*pi/1000; Rp_hp = -(min(dbhp(ceil(wphp/delta_w+1):1:501))); % Actual Passband Ripple fprintf('\nActual Passband Ripple is %.4f dB.\n', Rp_hp); As_hp = -round(max(dbhp(1:1:ceil(wshp/delta_w)+1))); % Min Stopband attenuation fprintf('\nMin Stopband attenuation is %.4f dB.\n\n', As_hp); %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- figure('NumberTitle', 'off', 'Name', 'Problem 8.35 Chebyshev-1 Highpass by dhpfd_bl function') set(gcf,'Color','white'); M = 1; % Omega max subplot(2,2,1); plot(wwhp/pi, maghp); axis([0, M, 0, 1.2]); grid on; xlabel('Digital frequency in \pi units'); ylabel('|H|'); title('Highpass Filter Magnitude Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.9441, 1]); subplot(2,2,2); plot(wwhp/pi, dbhp); axis([0, M, -100, 2]); grid on; xlabel('Digital frequency in \pi units'); ylabel('Decibels'); title('Highpass Filter Magnitude in dB'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-70, -61, -60, -1, 0]); set(gca,'YTickLabelMode','manual','YTickLabel',['70'; '61'; '60';'1 ';' 0']); subplot(2,2,3); plot(wwhp/pi, phahp/pi); axis([0, M, -1.1, 1.1]); grid on; xlabel('Digital frequency in \pi nuits'); ylabel('radians in \pi units'); title('Highpass Filter Phase Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]); subplot(2,2,4); plot(wwhp/pi, grdhp); axis([0, M, 0, 25]); grid on; xlabel('Digital frequency in \pi units'); ylabel('Samples'); title('Highpass Filter Group Delay'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0:5:25]); % ----------------------------------------------------- % method 2 % ----------------------------------------------------- % Digital lowpass Filter Specifications: [wpLP, wsLP, alpha] = hp2lpfre(wphp, wshp); prompt = 'Please input the type of digital lp filter: \n\n butter or cheby1 or cheby2 or ellip [butter]: '; type = input(prompt , 's'); [bhp, ahp] = dhpfd_bl(type, wphp, wshp, Rp, As) [C, B, A] = dir2cas(bhp, ahp) % ----------------------------------------------------- % method 3 cheby1 function % ----------------------------------------------------- % Calculation of Chebyshev-1 hp filter parameters: [N, wn] = cheb1ord(wphp/pi, wshp/pi, Rp, As); % Digital Chebyshev-1 Highpass Filter Design: [bhp, ahp] = cheby1(N, Rp, wn, 'high'); [C, B, A] = dir2cas(bhp, ahp) % Calculation of Frequency Response: %[dblp, maglp, phalp, grdlp, wwlp] = freqz_m(blp, alp); [dbhp, maghp, phahp, grdhp, wwhp] = freqz_m(bhp, ahp); % --------------------------------------------------------------- % find Actual Passband Ripple and Min Stopband attenuation % --------------------------------------------------------------- delta_w = 2*pi/1000; Rp_hp = -(min(dbhp(ceil(wphp/delta_w+1):1:501))); % Actual Passband Ripple fprintf('\nActual Passband Ripple is %.4f dB.\n', Rp_hp); As_hp = -round(max(dbhp(1:1:ceil(wshp/delta_w)+1))); % Min Stopband attenuation fprintf('\nMin Stopband attenuation is %.4f dB.\n\n', As_hp); %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- figure('NumberTitle', 'off', 'Name', 'Problem 8.35 Chebyshev-1 Highpass by cheby1 function') set(gcf,'Color','white'); M = 1; % Omega max subplot(2,2,1); plot(wwhp/pi, maghp); axis([0, M, 0, 1.2]); grid on; xlabel('Digital frequency in \pi units'); ylabel('|H|'); title('Highpass Filter Magnitude Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.9441, 1]); subplot(2,2,2); plot(wwhp/pi, dbhp); axis([0, M, -100, 2]); grid on; xlabel('Digital frequency in \pi units'); ylabel('Decibels'); title('Highpass Filter Magnitude in dB'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-70, -61, -60, -1, 0]); set(gca,'YTickLabelMode','manual','YTickLabel',['70'; '61'; '60';'1 ';' 0']); subplot(2,2,3); plot(wwhp/pi, phahp/pi); axis([0, M, -1.1, 1.1]); grid on; xlabel('Digital frequency in \pi nuits'); ylabel('radians in \pi units'); title('Highpass Filter Phase Response'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]); subplot(2,2,4); plot(wwhp/pi, grdhp); axis([0, M, 0, 25]); grid on; xlabel('Digital frequency in \pi units'); ylabel('Samples'); title('Highpass Filter Group Delay'); set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, M]); set(gca, 'YTickMode', 'manual', 'YTick', [0:5:25]);
运行结果:
采用dhpfd_bl函数,获得Chebyshev-1型数字高通滤波器,系统函数直接形式的系数
最小阻带衰减达到61dB,满足设计要求。
采用dhpfd_bl函数和cheby1函数(MATLAB自带)设计数字高通滤波器,幅度谱、相位谱和群延迟对比,相差不大。