ht2383_matlab_HW11_report

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Electrical Engineering

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Feb 20, 2024

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I save my code in problem1.m and problem2.m. Problem 1: Problem 1 says it’s a type1 filter, and the passband and stop-band edges are symmetric with respect to 𝜔 = 0.5pi, so I set frequency = [0 0.25 0.75 1]; % Passband and stopband edges symmetric so it can be symmetry around 0.5. It also says the weighting is equal in the pass-band and stop-band so I set weight = [1 1]; % Equal weighting in the passband and stopband . The following 3 graph are the impulse response, frequency response, phase and weighted response:

Code: % Type-I FIR Half-Band Filter Design using Remez exchange algorithm (Parks-McClellan) % Define frequency specifications

frequency = [0 0.25 0.75 1]; % Passband and stopband edges symmetric around 0.5pi amplitude = [1 1 0 0]; weight = [1 1]; % Equal weighting in the passband and stopband % Specify filter order order = 27; M = order - 1; alpha = M / 2; % Design the filter using Remez exchange algorithm h = firpm(M, frequency, amplitude, weight); % Frequency response analysis [H, weight] = freqz(h, 1, 512); weight = weight / pi; Aw = real(H .* exp(1i * pi * weight * alpha)); % Plot the impulse response figure(1); impz(h); title( 'Impulse Response' ); % Plot the frequency response figure(2); freqz(h, 1, 512); title( 'Frequency Response' ); % Plot the weighted response figure(3); plot(weight, Aw); title( 'Weighted Response' ); Problem 2: The magnitude response plot shows that the filter effectively meets the given specifications. The passband ripple (δ p ) and stopband attenuation (δ s) are within acceptable limits. The phase response plot shows the phase shift introduced by the

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filter across different frequencies. The phase shift is generally linear within the passband. The following 4 graphs are the magnitude response, phase response, impulse response and z-plane plot of problem2:

Code: % FIR Filter Design with Given Specifications % Given specifications delta_p = 0.05; delta_s = 0.05; ws = 0.4 * pi;

wp = 0.5 * pi; % Normalize frequencies ws_normalized = ws / pi; wp_normalized = wp / pi; % Define frequency specifications frequency = [0, wp_normalized, wp_normalized+0.01, ws_normalized]; amplitude = [1, 1-delta_p, 1-delta_p, 0]; weight = [1, 1]; % Ensure frequencies are non-decreasing frequency = sort(frequency); % Specify filter order order = 30; % Design the filter using firpm h = firpm(order, frequency, amplitude, weight); % Frequency response analysis [H, w] = freqz(h, 1, 1024, 'whole' ); % Plot the magnitude response figure; plot(w/pi, abs(H)); title( 'Magnitude Response' ); xlabel( 'Normalized Frequency (\omega/\pi)' ); ylabel( '|H(e^{j\omega})|' ); % Plot the phase response figure; plot(w/pi, angle(H)); title( 'Phase Response' ); xlabel( 'Normalized Frequency (\omega/\pi)' ); ylabel( 'Phase (radians)' );

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