[PD] a couple complex number abstractions

[padawan12]

Good stuff, thanks for solving these common complex operations
as useful abstractions Chuck.

Just to add a word to the previous discussion, I picked up a little
paperback called "Imagining Numbers" by Barry Mazur which is a great
idiots introduction to number theory, cartesian and polar forms and 
the basis for complex numbers, all done with geometry, diagrams and
hardly any equations. There's plenty of dinner party conversation
as a history mathematicians like Girolamo Cardano, Nicolas Chuquet,
Dal Faro and Bombelli which explains the context to needing imaginary
numbers to solve problems. When you understand why ordinary cardinal 
numbers can't solve certain problems it makes a whole lot more sense
why i was invented. I can reccomend this to any non-mathematician who
wants a gentle intro before getting stuck into something more formal.

a.



On Sat, 24 Feb 2007 22:50:41 -0600
"Charles Henry" <czhenry at gmail.com> wrote:

> Hi, list,
>   I put together a few abstractions I wanted to share.  These are just
> basic operations for complex arithmetic (I left out conjugate,
> addition, and subtraction, since I thought they were too basic).
> cmult~
> -- multiplies two complex signals; inlets are ordered from left to
> right: sig1-real, sig1-imaginary, sig2-real, sig2-imaginary (this is
> consistent for all the rest too)
> conj_mult~
> -- multiplies sig1 by the complex conjugate of sig2
> cnorm~
> -- computes sqrt(real^2+imag^2), Would this be more efficient using expr?
> cnormsq~
> -- computes real^2+imag^2.  Same question as cnorm~
> cdiv~
> -- divides sig1 by sig2.  Wherever sig2 is zero, the result is zero
> rather than undefined.  It is still not advised to use cdiv~ unless
> you have a signal that you know has all of its frequencies
> cdiv_thresh~
> -- accepts a threshold argument, and divides sig1 by sig2 whenever the
> complex norm squared of sig2 is greater than the threshold.  Returns
> zero otherwise.
> Later,
> Chuck
>