Re: Fwd: [fluid-dev] Purpose of dither?

[Z F]

--- Miguel Lobo <address@hidden> wrote:

> ---------- Forwarded message ----------
> From: Miguel Lobo <address@hidden>
> Date: May 9, 2007 3:02 PM
> Subject: Re: [fluid-dev] Purpose of dither?
> To: Mihail Zenkov <address@hidden>
> 
> Admittedly I have forgotten a lot about signal processing, but I'm
> not sure
> I agree with everything you're saying.
> 
> Roughly, dither convert harmonic distortion to noise.
> 
> 
> That much is clear.
> 
> If we just add
> > noise (random) to signal, distortion gone but noise will by
> modulated
> > by signal (correlate with signal). This noise not fully random.
> 
> 
> So, let's consider the sequence a[n] = rand() / (float)RAND_MAX -
> 0.5.
> 
> How is each value in this sequence not "fully random" and completely
> uncorrelated to all other values?  AFAICS, this sequence is white
> noise and
> if you add it to your audio, you get no modulation.
> 
> This is rectangle dithering.
> 
> 
> Certainly the probability distribution of each a[n] is uniform
> between - 0.5and
> 0.5, so it is rectangular.
> 
> To prevent this modulation and get pure white (fully random) noise
> (it
> > much better for human ears) not correlated with signal, we consider
> > previous dither value.
> 
> 
> If I'm not mistaken, we are in effect getting a new sequence:
> 
> b[n] = a[n] - a[n - 1]
> 
> And we are using this sequence for our dither.  Now, this is in
> effect
> applying a high pass filter to a[n], so if a[n] was white noise, b[n]
> will
> not be.
> 
> And, most certainly, each element of b[n] is not independent from the
> previous one.  For example, if you have b[n0] = 1, you know for a
> fact that
> a[n0] = 0.5 and a[n0 - 1] = -0.5.  Therefore, b[n0 + 1] = a[n0 + 1] -
> a[n0]
> = a[n0 + 1] - 0.5 < 0.  Therefore, b[n0] = 1 implies b[n0 + 1] < 0;
> these
> two elements are correlated and b[n] is not white noise.
> 
> What am I getting wrong here?


This is exactly my complaint about current implementation of dithering.
The noise is correlated drawn from a triangular distribution. My
understading, I could be wrong, that the design was that noise is drawn
from triangular distribution, but samples are uncorrelated. In the
latter case two calls to rnd are needed. But I could be mistaken in the
design goal.

ZF

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