[Pd] Complex audio signals

[Mathieu Bouchard]

On Wed, 21 Jun 2006, Chuckk Hubbard wrote:

>> 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?

No, your question was, is the mapping exactly 1-to-1 ? Well, it's not. 
However you won't actually hear a difference unless you really want to. If 
you want to hear a difference, use [-~] to take the difference between the 
original signal and the one that's supposed to be identical. Then use [*~ 
1000000]. You might be able to hear some noises.

If you're one of those people who think they hear the difference between 
16-bit and 24-bit audio, you might not need the [*~ 1000000] ;-)

>> 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?

The closest approximation is actually as exact as above. The reconstructed 
signal will sound like sin(440t) but only within that block. The 
continuation of sin(440t) to another block won't have the same FFT. 
Looping one block of that sin(440t) over and over won't sound like 
sin(440t) because what you're doing in effect is chopping parts of 
sin(440t) so that it becomes blocksize-periodic.

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

(other people already have given good answers about this in this thread)

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada