I have two random signals (created by matlab randn), where the second signal represents only a delayed version (by a fraction of an integer) of the first one:
x2[n] = x1[n-fd]
n ... discrete time index 0,1,2,3,4....N
fd ... fractional delay (0,1)
When I correlate the two signal and look for the fractional sample delay I obtain exactly the same value.
As soon I apply a amplitude quantization (1 and 2 bit) of the signals x1 and x2, the fractional sample delay I obtain by correlation is different. (see the plot below)
When I compare the input fraction delay with correlated delay (difference on the y-axis) for various fraction delays between 0 and 1 (x-axis) I see this patterns for 1 and 2 bit quantization. The 64 bit representation of the two signals (no quantization) shows no difference. So there is only a difference once I apply amplitude quantization.
Is this a known error when applying a quantization of a noise signal? If yes, would it be possible to point me to some literature or explain this behaviour?
Trying to understand your test:
Your x1 is generated from randn
your x2 is generated from FD of x1 (how?, do you apply FD filter).
if my samples are 0 and 1 only(1 bit) I don't see how I can get a value in between 0 & 1
Thanks for your question kaz. I realized that I missed a bandpass filter after my fraction delay application. So the problem wasn't the quantization but the fractional delay application carried out before.