If x is a discrete-time signal where x(n) is real for all n, then
X(w ) = X*(-w )
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(w ) = X*(-w )
where X = CTFT(x). Again, this follows easily from the definition of the CTFT.