I kindly ask for some help in providing an example of white noise series, different from Gaussian white noise. Especially, I would like to know if there is a recipe to generate a series of white noise from some distribution, which consists of variables "not independent, but uncorrelated". (Even though I know independent variables are the easiest way to achieve white noice.)

I know the "school example" of "not independent, but uncorrelated" variable: $Y = X^2$ (here is a description), but I am not sure this is the right hint here.

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    $\begingroup$ I think the key is to look at the defining characteristic of white noise: spectral power density. $\endgroup$ Commented Mar 3, 2014 at 14:58
  • $\begingroup$ I took a look at some papers about spectral density method of generating white noise and using it (?) would make my issue definitely not be a simple academic task I supposed it to be... $\endgroup$ Commented Mar 4, 2014 at 8:41

1 Answer 1


Any stationary zero mean distribution will be a white noise process as long as each of the samples are independent and identically distributed. The distribution itself has no effect on the process being white or not. A white noise process has a constant power spectral density, and the power spectral density is the Fourier Transform of the autocorrelation function. If the process produces zero mean independent and identically distributed samples, the autocorrelation function will be a unit sample function (scaled by the variance), which has a constant Fourier Transform.

Quantization noise is well approximated as a uniform white noise process. This is generated by rounding a sampled signal and will approximate a uniform white noise process well if the signal traverses several rounding boundaries from sample to sample. This can be understood intuitively by considering a sine wave: that has an amplitude that is several quantization levels and a frequency that is not an integer sub-multiple of the sampling frequency: where a sample lands between any two quantization levels given as $q$ will be uniformly likely in the span of $-q/2$ to $+q/2$ (or similarly if truncating instead of rounding will be uniform in the span of $0$ to $q$.

Another recipe for no independent but uncorrelated is to multiply a random signal by $j$.


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