[PD] imaginary numbers

[Mathieu Bouchard]

On Fri, 28 Aug 2009, brandt at subnet.at wrote:

> how is it possible to calculate with imaginary numbers in PD besides the 
> fft stuff.

basically, if you know that something is an imaginary number, you can use 
a real number in its place and just remember to multiply by square root of 
-1 in your head.

but if you want to combine real and imaginary numbers, then you need 
complex numbers, each of which is a real and an imaginary number.

let i be sqrt(-1)... then let's say you have two complex numbers, a+bi, 
c+di, as four floats. the sum is (a+c)+(b+d)i, that is you add the real 
parts together, and add the imaginary parts together. From this, you can 
guess how to subtract. The product formula is (a*c-b*d)+(a*d+b*c)i, which 
you can often see in Miller's FFT patches as a cluster of four [*~].

You can find more such formulas on Wikipedia, PlanetMath, MathWorld, or 
other, but if you can't find one or have trouble getting one to work, ask 
pd-list again.

Abstractions could have been made for some of these, especially *, /, exp, 
log, but I don't think any such library exists. GridFlow provides those 
operations as an external if you need something fast.

  _ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard, Montréal, Québec. téléphone: +1.514.383.3801