# [PD] fft beginner question

Martin Peach martin.peach at sympatico.ca
Wed Nov 21 20:17:52 CET 2007

```Frank Barknecht wrote:
>hard off hat gesagt: // hard off wrote:
>
> >
> > so, actually the FFT doesn't HAVE to use imaginary numbers....but they
> > are just used because "the complex-number system is
> > two-dimensional and that signals to be analysed are presumed to be
> > two-dimensional. They are decomposable into a sum of circular
> > trajectories"
> >
> > every day a bit more of this falls into place.
>
>An interesting thing to note is that the rfft outputs two signals,
>where seemingly only one signal comes in. How can that be?  Actually
>what comes into the rfft object are two values as well: One is the
>usual signal amplitude visible as a patch cord, and the other is:
>time!
>
>Time is not visible in Pd, it's just there and normally always walks
>on. But inside of a FFT-subpatch, time is frozen for the duration of a
>block (or rather: the "current time" is assumed to be infinite or
>eternal) to allow calculating a different representation: the
>time for too long this is actually quite mind-blowing as well.
>

I think it's more like:
The real part represents the energy you can measure and the imaginary part
is the part you can't measure. They oscillate back and forth but combine to
make a constant as long as the amplitude is constant. That way the energy of
the system is conserved and doesn't periodically magically disappear and
reappear. It's the same as the idea that total energy is conserved but is
made up of kinetic and potential components. Only the kinetic energy can be
measured directly. The potential energy can only be calculated. Say if you
stand at the top of a cliff you have a potential energy that is equal to the
kinetic energy you would have if you fell to the bottom. There is no real
instrument that can measure the potential energy so it's imaginary in a
sense, but the kinetic energy can be measured directly, so it's real.

Martin

```