《DSP using MATLAB》Problem 8.35

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 8.35 \n\n');

banner();
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% 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。