Complex numbers: fast cartesian to polar conversion

Question

Hi.

I'm looking for a fast way to turn an array of complex numbers into polar representation.

E.g, given a complex number X I want to turn it into polar representation like this:

  Q.phase    = atan2 (X.imag / X.real);
  Q.magniude = sqrt  (X.imag * X.imag + X.real * X.real);

I need to do this conversion around 400 thousand times per second on a fixed point DSP. My numbers are in 1.15.16 fixed point format and I'd like to keep it that way.

The DSP is very fast when I execute things in unconditional loops, e.g. when the loop-count known in advance. It crawls when it has to do subroutine calls and divisions. Cache misses are very slow as well, so I'd like not to use large lookup-tables if possible (4k would be okay.. I can set aside a bit of on-chip memory for that task).

Currently I process atan2 as a polynomial approximation and use the well-known bitwise algorithm for the integer square-root. That's not fast enough.

I have the feeling that there should be a more efficient way to get the result. Maybe some of the computations from sqrt and atan can be shared? Or is there an iterative way to get my results?

Answer 1

Check out this CORDIC DSP optimization Hard to tell if it helps in your case though.