### 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

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).

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