Draw amplitude spectrum of filter

i want to draw a amplitude spectrum of filter that has an amplitude of 5 in the range [0, 1] ; -20 (dB/octave) attenuation in

(1,6] and -60 (dB/octave) in the range (6, ...)

Answer 1

[Mathy]

Hi Hoa Luong,

Find the MATLAB code below according to the specification requested where there is an amplitude of 5 in the range [0, 1], -20 dB/octave attenuation in the range (1, 6], and -60 dB/octave attenuation in the range (6, …):

% Define the frequency range
f = logspace(-1, 2, 1000); % Frequency range from 0.1 to 100 Hz

% Initialize the amplitude spectrum
A = zeros(size(f));

% Define the amplitude spectrum
A(f <= 1) = 5; % Amplitude of 5 in the range [0, 1]
A(f > 1 & f <= 6) = 5 * (f(f > 1 & f <= 6) / 1).^(-20/20); % -20 dB/octave attenuation in (1, 6]
A(f > 6) = 5 * (6 / 1).^(-20/20) * (f(f > 6) / 6).^(-60/20); % -60 dB/octave attenuation in (6, ...)

% Plot the amplitude spectrum
figure;
semilogx(f, A, 'LineWidth', 2);
xlabel('Frequency (Hz)');
ylabel('Amplitude');
title('Amplitude Spectrum of the Filter');
grid on;

The graph yielded from the above MATLAB code is:

Hope this helps!