Let x(n) be an arbitrary signal, not necessarily real valued, with DTFT X(ω). What is the DTFT of   x*(–n)?

The Discrete Time Fourier Transform (DTFT) of a signal x(n) is given by X(ω).

The DTFT of the complex conjugate of the time-reversed signal, x*(-n), is given by the complex conjugate of the frequency-reversed spectrum, X*(-ω).

Here's the step-by-step process:

1. The DTFT of x(n) is X(ω) = Σ x(n) e^(-jωn) where the sum is over all n.

2. The time-reversed signal is x(-n).

3. The complex conjugate of a signal is denoted by , so the complex conjugate of the time-reversed signal is x(-n).

4. The DTFT of x*(-n) is then X*(-ω) = Σ x*(-n) e^(jωn) where the sum is over all n.

5. This is the complex conjugate of the frequency-reversed spectrum, X*(-ω).

So, the DTFT of x*(-n) is X*(-ω).