[Pd] Complex audio signals

[Chuckk Hubbard]

On 6/11/06, Piotr Majdak <piotr at 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.