Signal Analysis Workflow
Generate a noisy signal, analyze it with FFT, design a filter, and compare the cleaned result.
Step 1 — Generate a composite signal
Create a signal with two frequency components (10 Hz and 25 Hz) buried in noise. This mimics real-world sensor data where you must separate signal from noise.
t = linspace(0, 1, 512);
clean = sin(2*pi*10*t) + 0.5*sin(2*pi*25*t);
noisy = clean + 0.8*randn(1, 512);
plot(t, noisy);
title('Noisy signal')▶ Run in SimLabExpected output: A noisy waveform plot
Step 2 — Analyze with FFT
The Fast Fourier Transform reveals which frequencies dominate the signal. You should see clear peaks at 10 Hz and 25 Hz despite the noise.
t = linspace(0, 1, 512);
clean = sin(2*pi*10*t) + 0.5*sin(2*pi*25*t);
noisy = clean + 0.8*randn(1, 512);
N = length(noisy);
hz = (0:N-1) / N * 512;
mag = abs(fft(noisy)) / N;
half = floor(N/2);
hz_plot = hz(1:half);
mag_plot = mag(1:half);
plot(hz_plot, mag_plot);
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('Frequency Spectrum')▶ Run in SimLabExpected output: Spectrum with peaks near 10 Hz and 25 Hz
Step 3 — Design a low-pass filter
A 4th-order Butterworth filter with a 30 Hz cutoff (normalised to 0.117 at Fs=512 Sa/s, since fc/(Fs/2) = 30/256 ≈ 0.117) will keep the two signal tones and reject everything above.
Fs = 512; fc = 30; [b, a] = butter(4, fc/(Fs/2)); freqz(b, a, 256, Fs)▶ Run in SimLab
Expected output: Filter frequency response plot
Step 4 — Apply the filter and compare
Apply the filter to the noisy signal, then overlay both to see the improvement.
t = linspace(0, 1, 512);
clean = sin(2*pi*10*t) + 0.5*sin(2*pi*25*t);
noisy = clean + 0.8*randn(1, 512);
Fs = 512;
fc = 30;
[b, a] = butter(4, fc/(Fs/2));
filtered = filter(b, a, noisy);
subplot(2, 1, 1);
plot(t, noisy); title('Noisy');
subplot(2, 1, 2);
plot(t, filtered, 'b'); hold on;
plot(t, clean, 'r--');
legend('Filtered', 'Original clean');
title('Filtered vs. Original')▶ Run in SimLabExpected output: Two-panel comparison: noisy above, filtered + clean below
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