#### DTFT of Real Signals

The previous section established that the spectrum of every real signal satisfies

 (3.16)

I.e.,

 (3.17)

In other terms, if a signal is real, then its spectrum is Hermitian (conjugate symmetric''). Hermitian spectra have the following equivalent characterizations:
• The real part is even, while the imaginary part is odd:

• The magnitude is even, while the phase is odd:

Note that an even function is symmetric about argument zero while an odd function is antisymmetric about argument zero.

Next Section:
Real Even (or Odd) Signals