On 6/20/06, Mathieu Bouchard matju@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