Time Reversal
For any complex signal , , we have
(3.11) |
where .
Proof:
Arguably, should include complex conjugation. Let
(3.12) |
denote such a definition. Then in this case we have
(3.13) |
Proof:
(3.14) |
In the typical special case of real signals ( ), we have so that
(3.15) |
That is, time-reversing a real signal conjugates its spectrum.
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Symmetry of the DTFT for Real Signals
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Linearity of the DTFT