Definition of convolution of 2 complex signals

Hello,

Which of the following two definitions is correct for convolution
of 2 complex signals?

(1):
x1(t) convolve x2(t) = int from -inf to +inf [ x1(tau) x2*(t-tau) ]
dtau

(2):
x1(t) convolve x2(t) = int from -inf to +inf [ x1(tau) x2(t-tau) ]
dtau

Here x2*(.) is the complex conjugate of x2(.).

I would appreciate it if you could also point me to a textbook which
confirms your answer.

Thanks,

Carl

On 28 Apr, 03:55, carl.horto...@gmail.com wrote:
> Hello,
>
> Which of the following two definitions is correct for convolution
> of 2 complex signals?
>
> (1):
> x1(t) convolve x2(t) = int from -inf to +inf [ x1(tau) x2*(t-tau) ]
> dtau
>
> (2):
> x1(t) convolve x2(t) = int from -inf to +inf [ x1(tau) x2(t-tau) ]
> dtau
>
> Here x2*(.) is the complex conjugate of x2(.).

If you derive the convolution sum formula frm scratch, see

http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no&

with complex-valued x and h, the same form as in the real-valued
case pops out. No complex conjugates anywhere.

> I would appreciate it if you could also point me to a textbook which
> confirms your answer.

Can't remember having seen complex-valued convolutions having
been discussed in any textbooks.

Rune