# Can sample aliasing of strictly white noise lead to random walk (drift) in the sampled signal?

Aliasing of tones higher than the Nyquist frequency, and where the tone may have some degree of nonlinear distortion can appear as low frequency 'drift' or even near static bias in the sampled signal.

Also it's known that integration of a signal with a large component of white noise results in random walk - a 'drift' like behavior in the integrated signal.

So are there any possible situations combined with aliased sampling of signals with a significant white noise, or pink noise that can appear as low frequency drift in the sampled signal?

• white noise has "specific harmonics"? – robert bristow-johnson Mar 13 '15 at 18:37
• @robertbristow-johnson No. Please read more carefully - I mention the sampling of harmonics to set up the question of sampling white noise. As for white noise it has infinitely many harmonics, all of the same power. – docscience Mar 13 '15 at 18:41
• i think you need to modify your semantics. "harmonics" are spectral (sinusoidal) components of frequency that are integer multiples of a common fundamental. white noise can be thought of, at a probabilistic level to have infinitely many non-zero sinusoidal components. but that's a power spectrum P.O.V. white noise has infinite power (so it doesn't really exist). now we can make sense of the concept of sampling bandlimited white noise (which isn't really white, but at least is finite power). even if the band limit is higher than Nyquist (in which there will be aliasing). – robert bristow-johnson Mar 13 '15 at 18:55
• @robertbristow-johnson fair enough. I've edited and replaced harmonic with fundamental. I think in general sampled white noise (or rather wide band noise) just winds up as aliased noise across the sample bandwidth, but I'm curious if it might ever be possible where the aliased noise is more severly limited to a lower bandwidth over the sample band. – docscience Mar 13 '15 at 19:51
• @robertbristow-johnson perhaps if the white noise were 'riding' on top of a fundamental that is aliased to near zero frequency in the sample band. – docscience Mar 13 '15 at 19:54