On 6/11/06, Piotr Majdak piotr@majdak.com wrote:
Chuckk Hubbard wrote:
I'm teaching myself some DSP stuff, using Miller's Techniques, a Digital Filters book, and some other references, and I'm loving it. I am wondering, though, how one comes up with a complex audio signal for use in Pd. I want to experiment with [czero~], and I've also wondered where complex signals come from for [fft~].
I'm not sure I understand your question: Do you want to know why processing a real signal with the Fourier Transormation can result in a complex signal?
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.
I read a few pages further in Theory and Techniques, though, and found the suggestion of regarding a real signal as a complex signal plus its complex conjugate, and including the complex conjugate for every filter. I'm about to print out the next few pages and take a look at the rest of the chapter.
It doesn't seem like it would be possible to create a complex signal from a real one, but maybe there are ways to synthesize them?
A real signal can be regarded as a special case of a complex signal with the imaginary part set to zero. To create a complex signal just add an imaginary part, e.g. real signal x -> hilbert transformation of x -> x', which is the imaginary part of the analytic signal z=x + jx', z is complex now.
br, Piotr
OK, but Hilbert involves FFT, which involves distortion. And a signal with the imaginary part set to zero won't represent the same sines and cosines.