Cross-correlation of white noise process with its conjugate

[nitisha]

If w[n] are samples of the white gaussian noise process, I know that
E[w[n1] w[n2]] = 0 for a WGN process.

what would the following expression lead to:

E[w[n1] w*[n2]] = ?

Would it also be zero?

Thanks a lot!

 

[berkeman]

If w[n] are samples of the white gaussian noise process, I know that
E[w[n1] w[n2]] = 0 for a WGN process.

what would the following expression lead to:

E[w[n1] w*[n2]] = ?

Would it also be zero?

Thanks a lot!

Welcome to the PF.

What do you think the answer is and why? Also, is this for homework?

 

[FactChecker]

Are you talking about complex white noise where the real and imaginary parts are uncorrelated white noise processes? If so, the expected value should be 0.

 

[Baluncore]

If you reverse the samples in the time domain, you get the conjugate, = negative phase, in the frequency domain.

Why does it matter if a Gaussian white noise is played forwards or backwards in time?

 

[nitisha]

Thanks all! Got the answer.

If white noise is a complex random process, we say that E[w[n1] w*[n2]] = 0;
If it is a real random process, we say that E[w[n1] w[n2]] = 0

Generally speaking, the ensemble average of the auto-correlation function at times n1 and n2 of a WGN process is 0.