On Jun 20, 10:59 am, VijaKhara <VijaKh...@gmail.com> wrote:
> Hi all
>
> I am reading the Papoulis's book on Random Variable and getting
> confused with the following formula:
>
> X(t) is input of a linear system with impulse response h(t), Y(t) is
> its output.
> X(t) is a WSS Random Process
> ===> the Cross Correlation:  Rxy(to)= Rxx(to) * h*(-to).  where * is
> convolution, and h*(-to) is conjugate of h(-to).
>
> Now the density spectrum Sxy(omega)= Sxx(omega)H*(omega).
>
> I am confused, I think it should be Sxy(omega)= Sxx(omega)H*(-omega).,
> because the CTFT of x(-t) is X(-omega).
>
> AM I missing some point>
>
> Thanks

If your input signal is real-valued, then the Fourier transform is
symmetric, and hence H(w) = H(-w). If your input signal is complex
valued, then the transformation H'(w) = H(-w) is called spectral
inversion => the real and imaginary parts of x(t) are interchanged in
the time-domain.

Regards,
BERT.

Hi all

I am reading the Papoulis's book on Random Variable and getting
confused with the following formula:

X(t) is input of a linear system with impulse response h(t), Y(t) is
its output.
X(t) is a WSS Random Process
===> the Cross Correlation:  Rxy(to)= Rxx(to) * h*(-to).  where * is
convolution, and h*(-to) is conjugate of h(-to).

Now the density spectrum Sxy(omega)= Sxx(omega)H*(omega).

I am confused, I think it should be Sxy(omega)= Sxx(omega)H*(-omega).,
because the CTFT of x(-t) is X(-omega).

AM I missing some point>

Thanks