[Pd] Complex audio signals

[Chuckk Hubbard]

On 6/20/06, Mathieu Bouchard <matju at artengine.ca> wrote:
> On Mon, 19 Jun 2006, Chuckk Hubbard wrote:
>
> > Okay, I've read through some of the Fourier explanation in this Digital
> > Filters book, and I think I understand.  That was going to be one of my
> > next questions: if the data of the FFT actually has the same number of
> > possibilities as the audio data itself (by bit rate and block size), is
> > there then a 1 to 1 relationship, where no two audio blocks could have
> > the same FFT data.  I take the answer to be yes.
>
> For floats, it's not, but it's not terribly off the mark anyway (just
> rounding error).
>
> The mapping is only perfect in the (Real-based) Complex numbers and also
> in the Algebraic-numbers-based Complex numbers. However those systems are
> more difficult to compute with, so you find them in only a few apps, such
> as Mathematica and Maple. (Not even in Matlab, if I'm not mistaken).

I guess the question is, can anyone hear the difference?

> > So, the idea is just that the transform data is easier to read if there
> > is a harmonic relationship- not that the reconstructed signal will be
> > truer?
>
> The reconstructed signal will be fine. If instead of sin(440t) you get
> sin(420t)+0.2*sin(460t)+0.04*sin(500t)+... (completely made up example)
> then this only means that the latter is the closest approximation to the
> former in the context of that particular block size.

Can it be heard?


>
> > Too bad I go to an art school that would never pay for MathLab in a
> > million years.
>
> What do you need Matlab for?... PureData can do a lot of the job, and if
> it isn't enough, then add GridFlow (which has [#fft]).

I'm specifically curious about seeing integration and convolution,
although I haven't found how to do that in Octave yet.

-Chuckk

>
>  _ _ __ ___ _____ ________ _____________ _____________________ ...
> | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
> | Freelance Digital Arts Engineer, Montréal QC Canada
>


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