Code:
%% ------------------------------------------------------------------------
%% 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');
operation result:
Passband ripple and stopband attenuation, converting the question is an absolute value in dB units.
Non-normalized analog Butterworth low-pass filter, the direct form (rational functions) coefficients,
Converting the H (s) in series form, i.e. the form of the product of a series of second order subfilters
Analog filter amplitude spectrum, a phase spectrum and the impulse response sequence.
