I. Amidror

R. Soc. Royal Society Open Science 2: paper 140550. http://dx.doi.org/10.1098/rsos.140550

Sampling moiré effects are well known in signal processing. They
occur when a continuous periodic signal *g*(*x*) is sampled using a
sampling frequency *f*_{s} that does not respect the Nyquist condition,
and the signal-frequency f folds over and gives a new, false low
frequency in the sampled signal. However, some visible beating
artefacts may also occur in the sampled signal when *g*(*x*) is
sampled using a sampling frequency *f*_{s} which fully respects the
Nyquist condition. We call these phenomena sub-Nyquist artefacts.
Although these beating effects have already been reported in the
literature, their detailed mathematical behaviour is not widely
known. In this paper, we study the behaviour of these phenomena
and compare it with analogous results from the moiré theory.
We show that both sampling moirés and sub-Nyquist artefacts
obey the same basic mathematical rules, in spite of the differences
between them. This leads us to a unified approach that explains
all of these phenomena and puts them under the same roof. In
particular, it turns out that all of these phenomena occur when
the signal-frequency *f* and the sampling frequency *f*_{s}
satisfy *f* ≈ (*m*/*n*)*f*_{s}
with integer *m*, *n*, where *m*/*n* is a reduced integer ratio;
cases with *n* = 1 correspond to true sampling moiré effects.

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