Hi Mathieu
if I'm not wrong, as long as it is white it is flat in spectral terms but the distribution of amplitudes (probability density function, pdf) of white noise can be gaussian, cauchy, uniform, etc. Therefore I'm not sure that the spectrum is proportional to the pdf..
Alberto
On Sun, 20 Aug 2006, alberto.zin@poste.it wrote:
You are right. BTW, I already wrote an external for
gaussian noise
generation (it is an easy adaptation of the noise code +
Box-Muller
transform to make it gaussian - not distributed yet
because I've to
clean up the code, it is my first external ;-). But it did
not change it
very much :-( In addition it seems that using noise~ is
still ok to have
the desired slope in the spectrum...
Doesn't a Gaussian distribution have a spectrum proportional to its own density? That is, exp(-s^2/var)/sqrt(2*pi*var). That means that in the dB vs octave graph, it would appear as a quadratic instead of a straight line, and this doesn't match any of the examples shown in the Colors_of_noise article. Right?
_____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada
On Mon, 21 Aug 2006, alberto.zin@poste.it wrote:
if I'm not wrong, as long as it is white it is flat in spectral terms but the distribution of amplitudes (probability density function, pdf) of white noise can be gaussian, cauchy, uniform, etc. Therefore I'm not sure that the spectrum is proportional to the pdf..
Sorry, my mistake. I was completely confused. The spectrum that we're talking about is actually the expectation of a random spectrum, which is the expectation of amplitude of each frequency separately, which doesn't say much about which pdf each frequency has.
Btw, the spectrum of white noise is not flat, it's just that the expectation of the spectrum is flat.
What does "uniform" mean in a situation where things are understood in terms of amplitude and phase? are the amplitudes selected in polar coordinates with the correct jacobian? if instead cos and sin components are selected uniformly, then the maximum amplitude will only be possible for four phases, which are the four corners of a square shape.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada