《DSP using MATLAB》Problem 8.34

今天下了小雨，空气中泛起潮湿的味道，阴冷的感觉袭来，心情受到小小影响。

代码：

hp2lpfre子函数

function [wpLP, wsLP, alpha] = hp2lpfre(wphp, wshp)
% Band-edge frequency conversion from highpass to lowpass digital filter
% -------------------------------------------------------------------------
% [wpLP, wsLP, alpha] = hp2lpfre(wphp, wshp)
%   wpLP = passband edge for the lowpass digital prototype
%   wsLP = stopband edge for the lowpass digital prototype
%  alpha = lowpass to highpass transformation parameter
%   wphp = passband edge frequency for the highpass
%   wshp = stopband edge frequency for the highpass
%
%
if wphp <= 0
	error('Passband edge must be larger than 0.')
end

if wshp >= wphp
	error('Stopband edge must be smaller then Passband edge')
end

% Determine the digital lowpass cutoff frequencies:
wpLP = 0.2*pi;
alpha = -(cos((wpLP + wphp)/2))/(cos((wpLP - wphp)/2));
wsLP = angle(-(exp(-j*wshp)+alpha)/(1+alpha*exp(-j*wshp)));

　　dhpfd_bl子函数

function [b, a] = dhpfd_bl(type, wp, ws, Rp, As)
% IIR Highpass Filter Design using bilinear transformation
% -----------------------------------------------------------------------
% [b, a] = dhpfd_bl(type, wp, ws, Rp, As);
%   type = 'butter' or 'cheby1' or 'cheby2' or 'ellip'
%      b = numerator polynomial coefficients of highpass filter , Direct form
%      a = denominator polynomial coefficients of highpass filter, Direct form
%     wp = Passband edge frequency in radians;
%     ws = Stopband edge frequency in radians (wp < ws);
%     Rp = Passband ripple in +dB; Rp > 0
%     As = Stopband attenuation in +dB; As > 0
%
%
if isempty(type)
    str = 'butter';
end

switch type
    case 'butter'
    	[b , a] = butthpf(wp, ws, Rp, As); break;
    case 'cheby1'
    	[b , a] = cheb1hpf(wp, ws, Rp, As); break;
    case 'cheby2'
    	[b , a] = cheb2hpf(wp, ws, Rp, As); break;
    case 'ellip'
    	[b , a] = eliphpf(wp, ws, Rp, As); break;
    otherwise
        disp('Oh, input may be error!\n');
end

　　

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 8.34 \n\n');

banner();
%% ------------------------------------------------------------------------

% Digital Highpass Filter Specifications:
wphp = 0.6*pi;                 % digital passband freq in rad
wshp = 0.4586*pi;              % digital stopband freq in rad
Rp = 1;                      % passband ripple in dB
As = 15;                     % stopband attenuation in dB

%[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);

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 8.34 Chebyshev-1 Highpass')
set(gcf,'Color','white');
M = 2;                          % 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, 0.4586, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.8913, 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, 0.4586, 0.6, 1.4, 1.5414, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [-80, -23, -10, -1, 0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['80'; '23'; '10';' 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, 0.4586, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]);

subplot(2,2,4); plot(wwhp/pi, grdhp); axis([0, M, 0, 15]); grid on;
xlabel('Digital frequency in \pi units'); ylabel('Samples'); title('Highpass Filter Group Delay');
set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4586, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [0:5:15]);

% -----------------------------------------------------
%                  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)

　　运行结果：

cheb1hpf函数，得到Chebyshev-1型高通滤波器，系统函数直接形式的系数，阶数为4

直接形式转换成串联形式，系数

Chebyshev-1型高通滤波器，幅度谱、相位谱和群延迟响应

最小阻带衰减达到23dB，满足15dB的设计要求。