### Stretch Operator

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

*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).

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