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:

 (7.4)

where , with for odd, and for even. For example,

In this example, the first sample corresponds to time 0, and five zeros have been inserted between the samples corresponding to times and . Figure 7.7 illustrates zero padding from length out to length . Note that and could be replaced by and in the figure caption.
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 .7.8 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.
Next Section:
Causal (Periodic) Signals
Previous Section:
Stretch Operator