16. FFT and Spectral Analysis¶

Goal¶

Understand how to correctly interpret signal spectra in SDR experiments.

FFT is one of the most frequently used tools in SDR, but it is also one of the easiest tools to misuse.

1. Main problems¶

Spectral leakage¶

Leakage appears when the observed signal does not fit an integer number of periods inside the analysis window.

Typical symptoms:

energy spreads across nearby frequency bins;
a single tone does not look like a single narrow bin;
weak components may be hidden by leakage from stronger ones.

Frequency resolution¶

Resolution depends on FFT length and sampling rate.

Δf = Fs / Nfft

Where:

Fs: sampling rate;
Nfft: FFT size;
Δf: bin spacing.

Example from page 09: at Fs = 2.4 MHz and Nfft = 4096, Δf = 585.9 Hz, so a 200 kHz tone is reported at 199 804.7 Hz, the nearest bin. With Nfft = 65536 the bin is 36.6 Hz and the peak lands at 199 987.8 Hz. A longer FFT resolves frequency more finely, but it also needs a longer, stable recording.

Windowing¶

Windows reduce leakage at the cost of widening the main lobe.

Common windows:

rectangular;
Hann;
Hamming;
Blackman.

2. Analysis chain¶

flowchart TB
    classDef dsp fill:#DCFCE7,color:#0F172A,stroke:#16A34A,stroke-width:1px;
    classDef metric fill:#F1F5F9,color:#0F172A,stroke:#64748B,stroke-width:1px;

    SIG["IQ signal"]:::dsp
    DC["DC removal"]:::dsp
    WIN["Windowing"]:::dsp
    FFT["FFT"]:::dsp
    MAG["Magnitude / power spectrum"]:::metric
    PEAK["Peak and bandwidth estimation"]:::metric

    SIG --> DC --> WIN --> FFT --> MAG --> PEAK

3. Practical recommendations¶

Always document Fs, Nfft, window type, and scaling.
Use the same FFT settings when comparing experiments.
Do not estimate signal quality from a screenshot only.
Check whether the receiver is overloaded before trusting spectral peaks.
Combine FFT with SNR, EVM, or BER when possible.

4. SDR examples¶

Tone experiment¶

FFT is used to confirm tone frequency and estimate noise floor.

AM/FM experiment¶

FFT shows carrier, sidebands, and occupied bandwidth.

Digital modulation¶

FFT shows occupied bandwidth and spectral shaping.

5. Engineering conclusion¶

FFT is not just a plot. It is a measurement tool that requires correct scaling, windowing, and interpretation.