[PD] basic DSP stuff

[Chuckk Hubbard]

I understand complex numbers used to represent rotation, so as to encode
frequency in an easy to manipulate form, and I understand that the imaginary
part can be disposed of when converting back to real signals and nothing is
changed, but there's one bit that is hanging me up:
 Using i is just a convention, a way to keep from mixing the two numbers.
The square root of -1 is not really involved in any of it, because it
doesn't exist. So why, when you multiply Z1 and Z2, do i*sin(a) and i*sin(b)
multiply to -sin(a)sin(b)?
  Also, the decision (this is coming from Miller's "Theory and Techniques")
to multiply the complex constant A by the unit-value complex number Zn; this
is convenient, but it seems rigged. Instead of letting Z have whatever
amplitude it really has, in which case multiplying it (which already seems
forced) by itself changes its amplitude, you force it to be 1 and add on the
amplitude later. Nothing violated, but it seems artificial, like we fudge
the numbers to make it come out right. If it is artificial, and just a way
of simplifying sinusoid manipulation, then why even use artificial
mathematical operations to explain it?
 I already tried just moving ahead accepting these, but eventually something
always throws me.
  One more question... regarding how filters work, is there no intuitive way
to express it? No shortcut so that rpole~ and rzero~ will at least make
sense in theory before I push through all the math?
 -Chuckk


--
"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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