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 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 .^{7.9} 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.