On 2/7/15 8:54 AM, Vicki Melchior wrote:
Well, the point of dither is to reduce correlation between the signal and quantization noise. Its effectiveness requires that the error signal has given properties; the mean error should be zero and the RMS error should be independent of the signal. The best known examples satisfying those conditions are white Gaussian noise at ~ 6dB above the RMS quantization level and white TPDF noise at ~3dB above the same, with Gaussian noise eliminating correlation entirely and TPDF dither eliminating correlation with the first two moments of the error distribution. That's all textbook stuff. There are certainly noise shaping algorithms that shape either the sum of white dither and quantization noise or the white dither and quantization noise independently, and even (to my knowledge) a few completely non-white dithers that are known to work, but determining the effectiveness of noise at dithering still requires examining the statistical properties of the error signal and showing
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at the mean is 0 and the second moment is signal independent. (I think Stanley Lipschitz showed that the higher moments don't matter to audibility.)
but my question was not about the p.d.f. of the dither (to decouple both the mean and the variance of the quantization error, you need triangular p.d.f. dither of 2 LSBs width that is independent of the *signal*) but about the spectrum of the dither. and Nigel mentioned this already, but you can cheaply make high-pass TPDF dither with a single (decent) uniform p.d.f. random number per sample and running that through a simple 1st-order FIR which has +1 an -1 coefficients (i.e. subtract the previous UPDF from the current UPDF to get the high-pass TPDF). also, i think Bart Locanthi (is he still on this planet?) and someone else did a simple paper back in the 90s about the possible benefits of high-pass dither. wasn't a great paper or anything, but it was about the same point.
i remember mentioning this at an AES in the 90's, and Stanley *did* address it. for straight dither it works okay, but for noise-shaping with feedback, to be perfectly legitimate, you want white TPDF dither (which requires adding or subtracting two independent UPDF random numbers). and i agree with that. it's just that if someone wanted to make a quick-and-clean high-pass dither with the necessary p.d.f., you can do that with the simple subtraction trick. and the dither is not white but perfectly decouples the first two moments of the total quantization error. it's just a simple trick that not good for too much.
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