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.
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).