Noise Folding
# Noise Folding in Sampling: Out-of-Band Noise Becomes In-Band Noise
Noise folding occurs when sampling maps analog noise from different frequency regions onto the same sampled frequencies. The resulting baseband noise can include contributions from well beyond the desired signal band. A clean-looking analog baseband is therefore not sufficient to predict a sampled system’s noise floor.
This entry concerns noise present before a sampling operation. It is distinct from quantization noise, clock-jitter error and the noise shaping performed inside some converters.
## 1. Map the analog bands to sampled baseband
*Conceptual real-sampling spectrum map. Colored areas identify separate input contributions. Their stacked appearance after sampling represents addition of noise power, not addition of amplitude or new output-frequency layers.*
For a real sampler at fs, analog components separated by integer multiples of fs, or reflected around those multiples, can produce the same sampled frequency. A frequency can be mapped to the first Nyquist zone by choosing falias = |f − k fs| with an integer k that places the result between zero and fs/2.
At fs = 100 kS/s, 20 kHz, 80 kHz and 120 kHz all map to 20 kHz. Likewise, analog bands 10–30 kHz, 70–90 kHz and 110–130 kHz overlap across sampled 10–30 kHz. The second band reverses frequency order; for flat noise density its power still contributes throughout the same destination band.
## 2. Add independent noise in power units
*Analytical toy example using only the three stated noise bands. Each has a flat one-sided voltage-noise density of 10 nV/√Hz before filtering. The sampler has unity input-to-sampled voltage scaling. No ADC, filter or other noise is included.*
Three independent equal contributions give √(10² + 10² + 10²) = 17.32 nV/√Hz in their common destination band. This is a √3 density increase, or a threefold power increase, relative to one band alone. It is not a universal noise-folding factor; the analog spectrum and response determine how many weighted contributions reach each output frequency.
Suppose an idealized analog filter has unity amplitude transmission in 10–30 kHz and amplitude transmission 0.1 in each unwanted band. The unwanted powers are reduced by 0.1², and the combined density becomes √(10² + 1² + 1²) = 10.10 nV/√Hz. This calculation illustrates selected-band attenuation and does not specify a realizable filter or its own noise.
## 3. Put the attenuation before the relevant sampler
An analog antialias response reduces unwanted content before it loses its original frequency identity. Once noise has folded onto a signal frequency, an ordinary post-sampling frequency-selective filter acts on both together. It cannot distinguish their analog origins.
Digital filtering remains useful for removing sampled content outside the retained band. Before decimation, it also prevents new aliases caused by the lower digital sampling rate. That protection does not reverse aliases already created at the initial analog sampling step.
| Stage | What it can do | What must be checked |
|---|---|---|
| Analog antialias filter | Attenuate analog bands before sampling | Stopband rejection, passband error and settling |
| Sampler input network | Shape the spectrum reaching the sampling node | Analog bandwidth and aperture response |
| Digital filter | Remove unwanted sampled frequencies | Retained signal band and filter response |
| Decimation filter | Suppress content that would fold at the lower rate | Rejection before rate reduction |
## 4. Calculate the actual noise path
For a stationary noise model, the sampled spectrum contains shifted replicas of the filtered analog power spectrum. Use a consistent one-sided or two-sided PSD convention and the sampler’s scaling. Weight every contributing analog frequency by the actual pre-sampling transfer magnitude squared, then sum the independent powers at their sampled destinations.
Ideal unlimited white noise has infinite integrated power, so a useful calculation needs a physically meaningful analog bandwidth or roll-off. Include the driver amplifier, input network, ADC front-end bandwidth and any aperture averaging that applies. A −3 dB cutoff alone does not establish enough alias rejection.
Oversampling can move troublesome alias regions farther from the signal band and allow digital removal of still-separable noise. Its benefit depends on the analog spectrum, filter response and retained bandwidth. Sigma-delta modulator sampling rate is also different from final output data rate; architecture-specific internal filtering and alias rejection must be included.
## 5. Verify the sampled signal chain
Sweep representative out-of-band tones to confirm frequency mapping and attenuation, then integrate sampled noise over the intended output band. Keep gain, source impedance, sample rate and analog filtering fixed when comparing noise measurements. Check settling, distortion and driver loading after changing the antialias network.
The equivalent noise bandwidth describes integrated noise through a known response. Noise folding adds the question of where each analog frequency lands after sampling; both are needed for a defensible sampled-noise budget.
## References
- [Analog Devices: Why an Input Filter Is Necessary](https://www.analog.com/en/resources/faqs/FAQ_antialiasing_filter.html) — aliasing of signals and noise from higher Nyquist zones.
- [Analog Devices: CTSD Precision ADCs, Part 3](https://www.analog.com/en/resources/analog-dialogue/articles/ctsd-precision-adcs-part-3.html) — noise foldback, analog/digital filtering and architecture-dependent alias rejection.
- [Analog Devices: Maximize Sigma-Delta ADC Driver Performance](https://www.analog.com/en/resources/analog-dialogue/articles/maximize-the-performance-of-your-sigma-delta-adc-driver.html) — limiting broadband driver noise before sampling.