Noise model as Sinc function

Question

In "Fundamentals of signal processing: estimation theory", example 3.13 Kay has used a model of band-limited Gaussian noise with a uniform PSD and a sinc autocorrelation function. I expected the autocorrelation function to be a delta function. What I am missing?

Update

What I was missing is that the PSD does not have a phase...

Moreover, the autocorrelation function equals zero at the sampling locations, if the band limit equals the Nyquist frequency.

Answer 1

The autocorrelation of white Gaussian noise is a delta. When the noise is filtered or band-limited, as is the case here, the autocorrelation becomes a sinc.

This has interesting consequences, for example in telecommunications, where the noise at the output of a matched filter is uncorrelated only at certain time delays -- fortunately, the time delays we're interested in.