Field Guide · term

Also known as: undersampling, sub-Nyquist sampling, harmonic sampling, IF sampling

Bandpass sampling — also called undersampling — digitises a band-limited signal at a sample rate below its carrier frequency, deliberately using aliasing to fold a high-frequency band down onto baseband.1 The usual reading of the Nyquist theorem — sample at twice the highest frequency — is a special case; for a signal confined to a narrow band, what actually matters is twice the bandwidth, not twice the top frequency. That relaxation lets a modest ADC capture a signal sitting far above its own sample rate.

0 fs/2 fs 3fs/2 2fs zone 1 zone 2 zone 3 signal in zone 4 folds down to baseband
Half-sample-rate boundaries carve the spectrum into Nyquist zones; a signal in a higher zone aliases into zone 1, appearing at baseband.

How it works

Sampling at rate fs divides the frequency axis into Nyquist zones, each fs/2 wide. Any signal, wherever it truly lives, appears after sampling at a position folded into the first zone (0 to fs/2). In ordinary baseband sampling we keep the signal in zone 1 and treat aliasing as an enemy. Bandpass sampling instead places a narrowband signal in a chosen higher zone and lets it alias down on purpose, landing cleanly at baseband.

The conditions are strict:

  • The sample rate must be at least twice the signal’s bandwidth — the Nyquist rate for a bandpass signal.
  • The signal must fit entirely inside one Nyquist zone; if its band straddles a k·fs/2 boundary, it folds back on itself and is destroyed.
  • A sharp analog bandpass filter must precede the ADC so that only the wanted zone reaches it — otherwise noise and signals from every other zone alias down on top of the wanted one, and the ADC cannot tell them apart afterward.

Choosing fs so the band lands neatly in a zone (and knowing whether the zone is odd or even, which spectrally inverts the result) is the design work of bandpass sampling.

In practice

The technique’s appeal is that a signal at a high intermediate frequency — or even at RF — can be captured by an ADC clocked far slower than twice that frequency, saving cost and power. The limits are practical: the converter’s analog input bandwidth must actually reach the signal frequency (many ADCs sample a much wider analog band than their clock rate), and its aperture jitter must be small, because timing noise at a high input frequency translates into far more amplitude error than at baseband.

Relevance to SDR

Bandpass sampling underpins direct-sampling SDRs and IF-sampling designs, where a fast ADC grabs a whole band and software picks out channels. It is also the theory behind the RTL-SDR “direct sampling” HF hack: with the tuner bypassed, HF signals are undersampled by the RTL2832U and appear aliased into the first Nyquist zone. Understanding zones explains the spurious mirror signals such setups produce when the input filtering is weak.

GopherTrunk works on the IQ stream after the ADC and does not choose the sampling scheme, but the Nyquist-zone picture is the same one that governs aliasing artefacts in any capture it decodes.

Sources

  1. Undersampling — Wikipedia, on sampling below the carrier and folding a Nyquist zone to baseband via controlled aliasing. ↩

See also