Zero padding consists of extending a signal (or spectrum)
with zeros. It maps a length
signal to a length
signal, but
need not divide
.
Definition:
In this example, the first sample corresponds to time 0, and five zeros have been inserted between the samples corresponding to times
Figure 7.7 illustrates zero padding from length
out to length
. Note that
and
could be replaced by
and
in the
figure caption.
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Note that we have unified the time-domain and frequency-domain
definitions of zero-padding by interpreting the original time axis
as indexing positive-time samples from 0
to
(for
even), and negative times in the interval
.7.9 Furthermore, we require
when
is even, while odd
requires no such
restriction. In practice, we often prefer to interpret time-domain
samples as extending from 0
to
, i.e., with no negative-time
samples. For this case, we define ``causal zero padding'' as
described below.