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
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).