clc;
clear;
close all;

% ----------------------------------------------------------
% FIR Highpass Filter Design using Window Methods
% ----------------------------------------------------------

% Specifications
wp = 0.8 * pi;              % Passband edge frequency
ws = 0.7 * pi;              % Stopband edge frequency
wc = (ws + wp) / 2;         % Cutoff frequency
dw = abs(ws - wp);          % Transition width for HPF
M = ceil(1.8 * pi / dw) + 1; % No. of filter coefficients (make it odd)
n = linspace(0, M-1, M);    % Sample points

% ----------------------------------------------------------
% Ideal Highpass filter impulse response
% ----------------------------------------------------------
hd = (sin(pi * (n - (M-1)/2)) ./ (pi * (n - (M-1)/2))) ...
   - (sin(wc * (n - (M-1)/2)) ./ (pi * (n - (M-1)/2)));

% Handle n = (M-1)/2 case using L'Hôpital's Rule
hd((M-1)/2 + 1) = 1 - (wc / pi);

% ----------------------------------------------------------
% Window Functions
% ----------------------------------------------------------
W_rect = ones(1, M);        % Rectangular window
W_hamm = hamming(M)';       % Hamming window
W_hann = hanning(M)';       % Hanning window

% ----------------------------------------------------------
% Apply Windows to Ideal Impulse Response
% ----------------------------------------------------------
h_rect = hd .* W_rect;
h_hamm = hd .* W_hamm;
h_hann = hd .* W_hann;

% ----------------------------------------------------------
% Compute Frequency Response
% ----------------------------------------------------------
[H_rect, w] = freqz(h_rect, 1, 1024);
[H_hamm, ~] = freqz(h_hamm, 1, 1024);
[H_hann, ~] = freqz(h_hann, 1, 1024);

% Normalize frequency and magnitude
w = w / (2 * pi);
HN_rect = abs(H_rect) / max(abs(H_rect));
HN_hamm = abs(H_hamm) / max(abs(H_hamm));
HN_hann = abs(H_hann) / max(abs(H_hann));

% ----------------------------------------------------------
% Plot Results
% ----------------------------------------------------------
figure;
plot(w, 20 * log10(HN_rect), 'r', 'LineWidth', 1.5); hold on;
plot(w, 20 * log10(HN_hamm), 'b', 'LineWidth', 1.5);
plot(w, 20 * log10(HN_hann), 'g', 'LineWidth', 1.5);
grid on;
xlabel('\bf Normalized Frequency ----->');
ylabel('\bf Normalized Magnitude Response (dB) ----->');
title('\bf Highpass FIR Filter Designed Using Different Windows');
legend('Rectangular', 'Hamming', 'Hanning', 'Location', 'Best');

% ----------------------------------------------------------
% Display some info
% ----------------------------------------------------------
fprintf('Number of coefficients (M): %d\n', M);
fprintf('Cutoff frequency (rad): %.4f\n', wc);
fprintf('Transition width (rad): %.4f\n', dw);