#### Real Even (or Odd) Signals

If a signal is*even*in addition to being real, then its DTFT is also real and even. This follows immediately from the Hermitian symmetry of real signals, and the fact that the DTFT of any even signal is real:

*I.e.*,

*odd*and real, then its DTFT is odd and

*purely imaginary*. This follows from Hermitian symmetry for real signals, and the fact that the DTFT of any odd signal is imaginary.

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Proof of Aliasing Theorem

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DTFT of Real Signals