### Flip Operator

We define the flip operator by

 (7.1)

for all sample indices . By modulo indexing, is the same as . The operator reverses the order of samples through of a sequence, leaving sample 0 alone, as shown in Fig.7.1a. Thanks to modulo indexing, it can also be viewed as flipping'' the sequence about the time 0, as shown in Fig.7.1b. The interpretation of Fig.7.1b is usually the one we want, and the operator is usually thought of as time reversal'' when applied to a signal or frequency reversal'' when applied to a spectrum .

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