### Downsampling Operator

*Downsampling by*(also called

*decimation*by ) is defined for as taking every th sample, starting with sample zero:

*i.e.*,

*time-varying*operators. They can be modeled using time-varying

*switches*controlled by the sample index . The following example of is illustrated in Fig.7.10:

*sampling-rate conversion*to a lower sampling rate, in which a signal's sampling rate is lowered by resampling using bandlimited interpolation. To distinguish these cases, we can call this

*bandlimited downsampling*, because a lowpass-filter is needed, in general, prior to downsampling so that

*aliasing*is avoided. This topic is address in Appendix D. Early sampling-rate converters were in fact implemented using the operation, followed by an appropriate lowpass filter, followed by , in order to implement a sampling-rate conversion by the factor .

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Alias Operator

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Repeat Operator