# Symmetry for Real Signals

If *x* is a discrete-time signal where *x*(*n*) is real for
all *n*, then

*X*(*ω* ) =
*X^{*}*(

*-ω*)

where *X* = *DTFT*(*x*). We say that *X* is **conjugate
symmetric**. This property follows easily from the definition of the DTFT.

Similarly, if *x* is a continuous-time signal where *x*(*t*)
is real for all *t*, then

*X*(*ω* ) =
*X^{*}*(

*-ω*)

where *X* = *CTFT*(*x*). Again, this follows easily from the
definition of the CTFT.