For the following digital specifications

For the following digital specifications 1 ≤ |𝐻(𝑒 𝑗Ω)| ≤ 0.8 0 ≤ Ω ≤ 800 Hz |𝐻(𝑒 𝑗Ω)| ≤ 0.2 2.4 kHz ≤ Ω ≤ 4 kHz Write code to simulate

clear all;

close all;

clc;

% Given specifications

alphap = 20*log10(1) - 20*log10(0.8); % Passband attenuation

alphas = 20*log10(1) - 20*log10(0.2); % Stopband attenuation

op = 2 * tan(0.1 * pi); % Analog passband frequency

os = 2 * tan(0.3 * pi); % Analog stopband frequency

% Calculations

k1 = abs(os/op);

A1 = (10^(0.1*alphas) - 1)^0.5;

A2 = (10^(0.1*alphap) - 1)^0.5;

A = A1 / A2;

N = ceil(A / k1); % Order of the transfer function

k3 = 1 / (2 * N);

k4 = (10^(0.1*alphap) - 1)^k3;

oc = op / k4; % Cutoff frequency calculation

% Design the Butterworth filter

[b, a] = butter(N, oc);

% Plot frequency response

w = 0:.01:pi;

[h, om] = freqz(b, a, w, 'whole');

m = abs(h);

an = angle(h);

subplot(2,1,1)

plot(om/pi, m), grid, ylabel('Normalized Magnitude'), xlabel('Normalized Frequency');

subplot(2,1,2)

plot(om/pi, an), grid, ylabel('Angle'), xlabel('Normalized Frequency');

% Impulse invariant transformation

[bz1, az1] = impinvar(b, a, 1); % Impulse invariant transform of the function

% Bilinear transformation

[bz2, az2] = bilinear(b, a, 1); % Bilinear transform of the function