Definition: We define the flip operator by
which, by modulo indexing, is . The operator reverses the order of samples through of a sequence, leaving sample alone, as shown in Fig. 8.1a. Thanks to modulo indexing, it can also be viewed as “flipping” the sequence about the vertical axis, as shown in Fig. 8.1b. The interpretation of Fig. 8.1b 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 .