White noise example - but different from a Gaussian white noise signal

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.

• I think the key is to look at the defining characteristic of white noise: spectral power density. Commented Mar 3, 2014 at 14:58
• 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... Commented Mar 4, 2014 at 8:41

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 $$j$$.