Fourier Transform Question

One of the properties of the FT is


f(-t)  <-------> F(-w)

Does this mean that if we take the FFT of a signal and compute F(-w)
then inverse FFT we have a reverse-time representation?


K

>One of the properties of the FT is
>
>
>f(-t)  <-------> F(-w)
>
>Does this mean that if we take the FFT of a signal and compute F(-w)
>then inverse FFT we have a reverse-time representation?
>
>
>K


That's a property of the Fourier transform, not the discrete Fourier
transform.  So no.  Also, when you take the FFT of a signal, you don't get
F in w (omega), you get a discrete function.  Take a look at a table of DFT
properties.  For DFTs

x[-n] <---> X*[k]

kronecker@yahoo.co.uk wrote:

> Does this mean that if we take the FFT of a signal and compute F(-w)
> then inverse FFT we have a reverse-time representation?

See:

http://en.wikipedia.org/wiki/Nonlinear_optics#Optical_phase_conjugation

It can be done with real (optical) signals.  Even more, it is possible
to build a phase conjugate mirror with gain, such that the time reversed
signal has a larger amplitude than the signal going in.

-- glen