I always had this question in my mind: The autocorrelation function of the filtered white Gaussian noise is simply a sinc function (inverse transform of the output of a brickwall filter with bandwidth 1/2T). Now if we sample the autocorrelation function with rate 1/T, the discrete-time noise samples are uncorrelated due to the sinc function passing through 0s at the T-spaced sampling instants. However, T/2 spaced samples are correlated with each other and the discrete-time noise is not white anymore. What are the implications of this correlation in the subsequent receiver stages/algorithms? Thanks. _____________________________ Posted through www.DSPRelated.com

# Correlated noise samples

Started by ●August 22, 2013

Reply by ●August 22, 20132013-08-22

On 8/22/13 6:01 PM, commsignal wrote:> I always had this question in my mind: The autocorrelation function of the > filtered white Gaussian noise is simply a sinc function (inverse transform > of the output of a brickwall filter with bandwidth 1/2T).that's a premise that might be a little dubious. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Reply by ●August 22, 20132013-08-22

okay, i take back what i said previously. On 8/22/13 6:01 PM, commsignal wrote:> I always had this question in my mind: The autocorrelation function of the > filtered white Gaussian noise is simply a sinc function (inverse transform > of the output of a brickwall filter with bandwidth 1/2T).a very skinny sinc() function. this is not the discrete-time autocorrelation, but the continuous-time autocorrelation of what would come out of an ideal reconstruction of an gaussian p.d.f. random number generator.> Now if we sample > the autocorrelation function with rate 1/T, the discrete-time noise samples > are uncorrelated due to the sinc function passing through 0s at the > T-spaced sampling instants.yes. like a discrete-time impulse function (which is more like the discrete-time autocorrelation).> However, T/2 spaced samples are correlated with > each other and the discrete-time noise is not white anymore.well, what *is* the DTFT of x[n] = sinc(n + 1/2) ? it's gonna look *sorta* white.> What are the > implications of this correlation in the subsequent receiver > stages/algorithms?dunno. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Reply by ●August 24, 20132013-08-24

Hi, one very hands-on implication is that you can suppress white (wideband) noise by averaging nearby samples, but not if the noise samples are correlated. Replace the word "averaging" with "filtering" and we've got the profound insight that you can remove wideband noise with a filter, but not if it's inside your signal bandwidth. _____________________________ Posted through www.DSPRelated.com

Reply by ●August 24, 20132013-08-24

Umm, a slightly less profound interpretation is that if your noise is already lowpass filtered, adding another lowpass at or above the cutoff of the original might not do much good. This does not quite make into the realm of profundity, IMHO. Bob

Reply by ●August 24, 20132013-08-24

>> This does not quite make into the realm of profundity, IMHO.well, that was my point, more or less. Another way to look at it: filtering a narrow-band signal with a high-rate FIR filter is inefficient, as the taps become increasingly dependent on each other. _____________________________ Posted through www.DSPRelated.com