EECS20N: Signals and Systems

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.