EC02 · Sem 5 · Digital signal processing

FFT spectrum of a multi-tone signal

Aim: Use the FFT to find the frequencies hidden in a noisy signal.

🧪 Live simulation🧊 Real-time 3D bench⚠ Simulated values, not physical measurements

🔬 Virtual lab

Starting the lab…

📘 Theory

The fast Fourier transform turns N time samples into N/2 frequency bins of width fs/N. Each sinusoid becomes a peak; noise spreads evenly across all bins and sets the noise floor.

X[k] = Σ x[n]·e^(−j2πkn/N) · Δf = fs / N

🧰 Apparatus (virtual)

Signal source (two tones + noise)
FFT analyser

📝 Procedure

Run with the two-tone signal and read both peaks
Raise the noise and watch the floor rise
Change the window and compare leakage
Compute the bin width fs/N

Observations and result (kept on this device)

🎤 Viva questions

Why is the FFT faster than the DFT

It needs N·log₂N operations instead of N².

What is spectral leakage

Energy spreading into nearby bins when a tone does not fit a whole number of cycles in the window.

🛡️ Safety

Virtual lab. With real RF equipment, respect exposure limits, never transmit without a licence, and keep antennas away from people.