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Stretch OperatorUnlike 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.

Definition:Astretch by factoris 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. 8.4. The example is

The stretch operator is used to describe and analyze

upsampling, i.e., increasing the sampling rate by an integer factor.