[Pd] Complex audio signals

[Piotr Majdak]

Chuckk Hubbard wrote:

> On 6/11/06, Piotr Majdak <piotr at majdak.com> wrote:
> 
> No, I want to know why there is an [fft~] object that is not for real
> signals, and how to make something into a complex signal.

Consider following situation: a signal x should be filtered with two filters hL 
and hR to signals yL and yR for presentation via headphones.

Using complex signals you can do it with one filtering task only.
- Create a complex filter: hZ = hL + ihR
- Perform the fFiltering yZ = IFT(FT(x)*FT(hZ))
- yZ is yL + iyR now.

Result: only _one_ filtering for _two_ signals, but you need a _complex_ fourier 
transformation ;-)

> OK, but Hilbert involves FFT, which involves distortion.  

FT is just one way to calculate the HT. A good approx. can be achieved with a 
FIR filter. The result will be a real signal, but you consider it as the 
imaginary part of what ever you want (here: analytic signal).

And I really don't know what do you mean by "FFT, which involves distortion". 
You don't mean distortions as in "nonlinear distortions", don't you?

> And a signal
> with the imaginary part set to zero won't represent the same sines and
> cosines.

Same as what? Sorry, don't understand it...

br, Piotr


-- 
Piotr Majdak
Institut für Schallforschung
Österreichische Akademie der Wissenschaften
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