Re: randomized white noise = white noise?

Oh, bull, Don. If you multiply a sinewave, or a DC level, by a good
random signal, the result will certainly be more random (have energy
distributed more uniformly across the spectrum, and have less
correlation from sample to sample) than the sinewave or DC level. In
the case of the sinewave, of course, the time-domain then looks like
random in a sine envelope. Re-ordering samples of a DC level does not
randomize it, of course, but randomly reordering samples of a sine
results in spectrally flat output, though with the same amplitude
distribution as the original sinewave of course.

Sampled-domain pink noise or noise filtered with "arbitrary peaks and
valleys" in the spectrum is no longer random; it has correlation from
sample to sample. Randomly reordering the samples removes that
correlation. XOR-ing digitized samples of any signal with uncorrelated
random digital samples will likewise result in a signal with
statistically constant energy per unit bandwidth.

There are even a few examples of combinations of random generators that
yield "better" randomness, though as you noted, it's only "almost
certainly" in that case...

Cheers,
Tom

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