Flip Operator

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Flip Operator

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Flip Operator



Definition: We define the flip operator by

\

which, by modulo indexing, is $x(N-n)$. The $\ operator reverses the order of samples $1$ through $N-1$ of a sequence, leaving sample $0$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 $x$ or “frequency reversal” when applied to a spectrum $X$.
Figure 8.1:Illustration of $x$ and $\for $N=5$ and two different domain interpretations: a) $n\. b) $n\.
\

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