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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
.
Figure 7.1:
Illustration of
and
for
for the two main
domain conventions:
a)
.
b)
.

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