[PD] basic DSP stuff
Chuckk Hubbard
badmuthahubbard at gmail.com
Sat Nov 12 02:18:57 CET 2005
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))
You could indeed say that "entity of your choice = 1/0". But you need a
> compelling reason why such a quantity is useful, and various proofs on how
> it is derived and used. All math depends on certain assumptions and those
> assumptions are different in different circumstances - aka Euclidian
> geometry and topology.
>
> Actually, you can say 1+2 = 12 ... and if you are putting together a
> string in a programming language, that makes sense and is useful, it is a
> valid operation. Many object oriented programming languages let you
> redefine basic symbols such as "+ - * /". But string addition wouldn't be
> very helpful for doing audio math calculations.
>
> So if you want to define your own i, go ahead, but don't you think your
> calculations are going to turn out better if you follow the normal math
> definitions?
>
> ~David
>
> > What I'm getting at is that expressing rotation as complex numbers is no
> > different than using cartesian coordinates. Why, when you multiply two
> > points, would one of the multiples turn negative?
> > I see no reason you couldn't say i = 1/0. Then 4*0*i=4. That makes as
> much
> > sense.
> >
>
>
--
"It is not when truth is dirty, but when it is shallow, that the lover of
knowledge is reluctant to step into its waters."
-Friedrich Nietzsche, "Thus Spoke Zarathustra"
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