[PD] imaginary numbers
matju at artengine.ca
Fri Aug 28 17:34:19 CEST 2009
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
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.
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