[PD] basic DSP stuff

[Mathieu Bouchard]

On Sat, 12 Nov 2005, Frank Barknecht wrote:

> Chuckk Hubbard hat gesagt: // Chuckk Hubbard wrote:
> >  I don't much care, I don't want to define my own math, I just want to know
> > why we mix the real and imaginary parts of a product in one specific case.
> >  Z1*Z2=r1r2(cos a + isin a)(cosb + isin b)
> > = r1r2 (cosa*cosb)-(sina*sinb) + i(sina*cosb + cosa*sinb)
> > = r1r2 (cos(a + b) + isin(a + b))
> 
> While doing computations, you can consider i to behave just like a
> "normal" real number, except if you multiply it with itself, then the
> result is i*i=-1. That's all there is to know about i.

Well, I don't think you can expect i to behave like a normal Real number. 

I think it might be clearer as: a complex number is a polynomial of the
variable i with Real coefficients, modulo (i^2+1). Here the complex number
is the polynomial itself, not any evaluation of the polynomial, so it
doesn't matter at all what the value of i may be in Real terms: it's a
dummy variable.

____________________________________________________________________
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
Freelance Digital Arts Engineer, Montréal QC Canada