Unlike all previous operators, the
operator maps
a length signal to a length
signal, where and are integers.
We use ``'' instead of ``'' as the time index to underscore this fact.

Figure 7.6:
Illustration of
.

A stretch by factor is defined by

Thus, to stretch a signal by the factor , insert zeros between each
pair of samples. An example of a stretch by factor three is shown in Fig.7.6.
The example is

The stretch operator is used to describe and analyze upsampling,
that is, increasing the sampling rate by an integer factor.
A stretch by followed by lowpass filtering to the frequency band
implements ideal bandlimited interpolation
(introduced in Appendix D).