Sampling, Nyquist and aliasing
An SDR turns the analogue wave into numbers: it measures the signal very fast, at regular intervals. That's sampling, and its pace is the sample rate (samples per second, Sps — usually MSps).
The golden rule: Nyquist
The Nyquist theorem sets the limit: to faithfully represent a band of width B, you must sample at least at 2·B. Thanks to I/Q (complex) samples, the rule gets even simpler for an SDR: sample rate = width of the observed window. 20 MSps → you see ~20 MHz around the centre frequency.
| Sample rate | Window | Typical use | USB throughput |
|---|---|---|---|
| 2 MSps | 2 MHz | one FM station, ADS-B, fine zoom | 4 MB/s |
| 4 MSps | 4 MHz | the whole 868 ISM band | 8 MB/s |
| 8 MSps | 8 MHz | a good slice of the FM band | 16 MB/s |
| 20 MSps | 20 MHz | the 2.4 GHz chaos, drone hunting | 40 MB/s |
Wide = overview but more CPU/USB load and a higher apparent per-bin noise floor; narrow = detailed zoom and a relaxed machine. The right reflex: wide to search, narrow to study.
Aliasing: the spectrum's ghost
If a signal exceeds the window it doesn't vanish: it folds back inside, at a false position. That's aliasing — a ghost that looks like a real signal but isn't there.
Concrete example: an 8 MHz window centred on 100 MHz (96–104 MHz). A strong transmitter at 105 MHz, poorly filtered, can reappear mirrored near 103 MHz — where nobody is transmitting.
SDRs limit this with an analogue anti-aliasing filter before the sampler (the HackRF sets one automatically at ~75% of the sample rate). But it remains a classic trap. Tell-tale signs of an alias:
- the peak moves the wrong way when you change the centre frequency;
- it moves twice as fast as the others;
- it disappears when you widen the sample rate.
And what about bits?
Each measurement is coded on a finite number of bits — that's quantisation. A HackRF codes on 8 bits: 256 levels, i.e. a theoretical dynamic range of about 48 dB between the smallest and the largest signal measurable at the same time. A 12-bit SDR (Airspy, SDRplay) gains ~24 dB: it tolerates a strong transmitter without crushing the weak one next door. That's why gain setting matters so much on an 8-bit receiver: it places your 48 dB window at the right floor of the building.
Your turn
- You want to watch the whole FM band (88–108 MHz) at once. Minimum sample rate? (20 MSps, centred on 98 MHz.)
- At 2.4 MSps, how many bytes per second does an RTL-SDR output? (2.4 M × 2 = 4.8 MB/s.)
- A peak slides left as you tune right. Real signal or alias? (Alias — or saturation; lower the gain to settle it.)
👉 See bandwidth in action: The 2.4 GHz chaos
Next: Les échantillons I/Q — why samples are complex numbers.