MATLAB program for the design of Chebyshev digital low pass filter using

Write a MATLAB program for the design of Chebyshev digital low pass filter using the following specification:

0.9 ≤│H(ejw)│≤ 1 0 ≤ w ≤ 0.3π

│H(ejw)│≤ 0.15 0.5π ≤ w ≤ π

Answer 1

[Vishwa]

15. Write and execute a MATLAB program to design a Chebyshev digital IIR low pass filter using Impulse invariant transformation to satisfy the following specifications:

T = 1 sec; 0.9 <= H(e ^ (jw)) <= 1 ; for 0 <= omega <= 0.25pi H(e ^ (jw)) <= 0.24 for for 0.5pi <= omega <= pi

[Vishwa]

% Given specifications
T = 1; % Sampling period
Wp = 0.25 * pi; % Passband edge frequency
Ws = 0.5 * pi; %Stopband edge frequency
Rp = -20 * log10(0.9); % Passband ripple in dB
Rs = -20 * log10(0.24); % Stopband attenuation in dB
% Pre-warp the frequencies for the bilinear transformation
Wp_warped = 2 / T * tan(Wp / 2); Ws_warped = 2 / T * tan(Ws / 2);
% Calculate the analog filter order and cutoff frequency
[n, Wn] = cheb1ord(Wp_warped, Ws_warped, Rp, Rs, 's');
% Design the analog Chebyshev Type I filter
[z, p, k] = cheby1(n, Rp, Wn, 'low', 's');
% Convert to transfer function form
[bs, as] = zp2tf(z, p, k);
% Perform Impulse Invariant Transformation
[bd, ad] = impinvar(bs, as, 1 / T);
% Plot the frequency response of the digital filter
fvtool(bd, ad);
% Display the filter coefficients
bd
ad