《DSP using MATLAB》Problem 8.12

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 8.12 \n\n');

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

Wp = 500; Ws = 2000; Rp = 0.25; As = 50;
Fp = Wp/(2*pi);
Fs = Ws/(2*pi);

Ripple = 10 ^ (-Rp/20)
Attn = 10 ^ (-As/20)

% Analog filter design:
[b, a] = afd('butter', Fp, Fs, Rp, As);
%[b, a] = afd_butt(Wp, Ws, Rp, As);

% Calculation of second-order sections:
[C, B, A] = sdir2cas(b, a);

% Calculation of Frequency Response:
[db, mag, pha, ww] = freqs_m(b, a, 2500);

% Calculation of Impulse Response:
[ha, x, t] = impulse(b, a);

%% -------------------------------------------------
%%                    Plot
%% -------------------------------------------------  

figure('NumberTitle', 'off', 'Name', 'Problem 8.12 Analog Butterworth lowpass')
set(gcf,'Color','white');
M = 1.0;                          % Omega max

subplot(2,2,1); plot(ww, mag);  grid on; axis([-2100, 2100, 0, 1.2]);
xlabel(' Analog frequency in rad/sec units'); ylabel('|H|'); title('Magnitude in Absolute');
set(gca, 'XTickMode', 'manual', 'XTick', [-500, 0, 500, 2000]);
set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.003, 0.97, 1]);

subplot(2,2,2); plot(ww, db);  grid on; %axis([0, M, -50, 10]);
xlabel('Analog frequency in rad/sec units'); ylabel('Decibels'); title('Magnitude in dB ');
set(gca, 'XTickMode', 'manual', 'XTick', [-500, 0, 500, 2000]);
set(gca, 'YTickMode', 'manual', 'YTick', [-50, -1, 0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['50';' 1';' 0']);

subplot(2,2,3); plot(ww, pha/pi);  grid on; axis([-2100, 2100, -1.2, 1.2]);
xlabel('Analog frequency in rad/sec nuits'); ylabel('radians'); title('Phase Response');
set(gca, 'XTickMode', 'manual', 'XTick', [-500, 0, 500, 2000]);
set(gca, 'YTickMode', 'manual', 'YTick', [-1:0.5:1]);

subplot(2,2,4); plot(t, ha); grid on; %axis([0, 30, -0.05, 0.25]);
xlabel('time in seconds'); ylabel('ha(t)'); title('Impulse Response');

　　运行结果：

通带ripple和阻带衰减，将题中的dB单位转换为以绝对值为单位。

非归一化模拟Butterworth低通滤波器，直接形式（有理函数）的系数，

将H(s)转换成串联形式，即一系列二阶子滤波器的乘积形式

模拟滤波器的幅度谱、相位谱和脉冲响应序列。