Chuckk Hubbard wrote:
On 6/11/06, Piotr Majdak piotr@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