Re: Algorithm to achieve this result?

On Jul 29, 11:45 am, Gene <gene.ress...@xxxxxxxxx> wrote:
On Jul 29, 5:01 am, mike3 <mike4...@xxxxxxxxx> wrote:



Hi.

I was trying to make a program that would take a bifurcation diagram,
like this:

http://www.chaos-101.com/wp-content/uploads/2008/01/bifurcation_diagr...

(not a picture file, but calculated on-the-fly from the mathematical
formula (e.g. logistic map,
quadratic map, etc.) so you can tweak parameters, get the smoothest/
finest resolution, etc.
with minimum hassle.)

interpret it as a spectral graph like this:

http://www.icsi.berkeley.edu/Speech/mr/images/headset_spectrogram.gif

and turn that into listenable audio. What sort of algorithm would do
this? I could calculate
a slice of the spectral graph for a given sample and store that in an
array, but how do I turn
that into amplitude-representation (waveform)? My guess is it would
involve an inverse Fourier
transform, but how exactly would I use it to do this? Analyzing source-
codes for programs
that do similar stuff is not exactly an easy endeavor. Where could I
find a _good_ description
of this algorithm that is easy to follow?

A power spectrum has all phase information removed, leaving only
magnitude by frequency.  So it's useless for recreating sound.  You
could certainly create a vector of complex numbers from the
bifurcation diagram and apply a discrete inverse fft that.  You would
have to make an assumptions about periodicity, the simplest being that
the signal repeats endlessly on the time axis, so you essentially have
an endless loop recording.  You're almost certain to be disappointed
in the results, however.  It's likely to sound like endless noise.

Have a look at this:

http://en.wikipedia.org/wiki/Spectrogram#Creating_sound_from_a_spectrogram

But I'm wondering about algorithms. How does one actually _do_ that?
.