🚀 go-pugleaf

In article <21901@unix.SRI.COM> shimizu@unix.SRI.COM (Dan Shimizu) writes:

   I'm attempting to do an analysis of a multi tone signal using a AT&T
   DSP32c chip and accompanying algorithims.  I'm most interested in the
   phase relationships between the tones.  To accomplish this I'm performing
   a 64 point real fft and then calulating the phase angle of the bins of
   interest.  The problem: the phase calculation is taking too long.

   -- stuff deleted --

   Because this is such a basic problem (finding the phase angle of a complex
   number), I'm hoping there exits a well-known speedy algorithim to accomplish
   it....does there?

I suggest using the CORDIC rotational technique. It is fast, simple and
computationally stable. The basic CORDIC algorithm is an iterative method which
uses only integer additions, subtractions and shift operations. I used it for
converting complex vectors (inphase component, quadrature component) to polar
form (envelope, phase).

I particulary like CORDIC because there is no need to perfrom very compicated
or expensive operations. I didn't even have to use a DSP, an old 8086 was just
fine, to get a throughput of several Ksamples per second, using 16-bit integer
arithmetic in a high-level language.

The original article describing CORDIC is:

Jack E. Volder, "The CORDIC Trigonometric Computing Technique," IRE
Transactions on Electronic Computers, pp.330-334, September 1959 (!)

CORDIC and its descendents are widely used to compute all kinds of other
complicated functions, such as trigonometric, exponential and hyperbolic
functions. I believe that for instance the intel 80x87 numerical coprocessors
and HP RPN calculators use the CORDIC principle.

Hope this is helpful.

--
Eric Aardoom (aardoom@donau.et.tudelft.nl)
Pulse and Digital Electronics Lab
Department of Electrical Engineering
Delft University of Technology
The Netherlands