Complete Filter Design Workflow in MATLAB

Complete Filter Design & Analysis Workflow

% Specs
fs = 8000; fp = 1000; fs_stop = 1500;  % Hz
Ap = 1; As = 50;  % dB

% Normalize
wp = 2*fp/fs; ws = 2*fs_stop/fs;

% FIR Design (Kaiser window)
[N, beta] = kaiserord([fp fs_stop]/(fs/2), [1 0], [10^(-Ap/20) 10^(-As/20)]);
b_fir = fir1(N, wp, kaiser(N+1, beta));
fvtool(b_fir, 1, 'Fs', fs);

% IIR Design (Elliptic - minimum order)
[N, Wn] = ellipord(wp, ws, Ap, As);
[b_iir, a_iir] = ellip(N, Ap, As, Wn);
sos = tf2sos(b_iir, a_iir);  % Critical for implementation!
fvtool(sos, 'Fs', fs);

% Compare orders
fprintf('FIR order: %d, IIR order: %d\n', N, N);

% Apply filter
x = randn(1, 10000);
y_fir = filter(b_fir, 1, x);
y_iir = filter(sos, x);  % Use SOS form

% Verify frequency response
[h_fir, f] = freqz(b_fir, 1, 1024, fs);
[h_iir, f] = freqz(sos, 1024, fs);
figure; plot(f, 20*log10(abs(h_fir)), f, 20*log10(abs(h_iir)));
legend('FIR', 'IIR'); ylabel('Magnitude (dB)');

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Pole-Zero Analysis

% Given difference equation: y[n] - 0.5y[n-1] = x[n] + 0.25x[n-1]
b = [1, 0.25];
a = [1, -0.5];

% Pole-zero plot
zplane(b, a);

% Stability check
poles = roots(a);
fprintf('Poles: %s\n', mat2str(poles));
fprintf('Stable? %s\n', mat2str(all(abs(poles) < 1)));

% Frequency response
freqz(b, a, 1024, fs);

% Impulse response
impz(b, a, 50);

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Spectrogram (Time-Frequency Analysis)

% Non-stationary signal: chirp
fs = 1000;
t = 0:1/fs:2;
x = chirp(t, 0, 2, 400);  % 0 to 400 Hz over 2 seconds

% Spectrogram
figure;
spectrogram(x, 256, 128, 256, fs, 'yaxis');
title('Chirp Signal Spectrogram');
colorbar;

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Complete Lab Template

% =============================================
% DSP LAB: [Experiment Name]
% Course: CSE 410
% =============================================

clear; clc; close all;

%% Parameters
fs = 8000;        % Sampling frequency
N = 1024;         % FFT size / signal length

%% 1. Signal Generation
% [Generate test signals here]

%% 2. Time-Domain Analysis
% [Plot signals, compute statistics]

%% 3. Frequency-Domain Analysis
% [FFT, manual DFT verification]

%% 4. Filter Design
% [Design FIR/IIR per specs]

%% 5. Filter Application
% [Filter signals, compare input/output]

%% 6. Verification
% [Check specs met, stability, etc.]

%% 7. Results & Discussion
% [Plots, observations, conclusions]

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Key MATLAB Functions Cheat Sheet

Category	Functions
Signal Gen	sin, cos, square, sawtooth, chirp, randn, zeros, ones
Time Ops	shift, flip, upsample, downsample, interp, decimate
Statistics	mean, std, var, cov, corrcoef, skewness, kurtosis
Transforms	fft, ifft, fftshift, dftmtx
Filter Design	fir1, fir2, firpm, kaiserord, butter, cheby1, cheby2, ellip, buttord, cheb1ord, ellipord
Filter Analysis	freqz, zplane, impz, grpdelay, tf2sos, sos2tf
Filtering	filter, filtfilt (zero-phase), filter2
Spectral	pwelch, periodogram, spectrogram, cpsd
Matrix	eye, zeros, ones, reshape, toeplitz, find, mean

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