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From: shimizu@unix.SRI.COM (Dan Shimizu)
Newsgroups: comp.dsp
Subject: phase of complex number
Message-ID: <21901@unix.SRI.COM>
Date: 5 Mar 91 03:55:04 GMT
Reply-To: shimizu@unix.sri.com (Dan Shimizu)
Organization: SRI International, Menlo Park, CA
Lines: 36

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.

My current (lenghty) solution is:

1) take complex number a + bj
2) perform abs(b/a)  (my atan(x) routine only works for x>0)
3) do atan(abs(b/a)) lookup
4) using the signs of the original a and bj, translate atan(abs(b/a)) to
   the proper quadrant.
5) Done!

The most time wasted seems to be in step 4), I must do a multi-level
if else construct to find the proper quadrant and perform the appropriate
translation, is there an easy way to do this?

Someone else suggested that the atan(abs(b/a)) lookup be done as a 
lookup versus abs(a) and abs(b), so the division would be unecessary.
The problem I'm having with this is trying to bound a and b so I
can generate the proper table. (Using b/a normalizes the process, so
the lookup table does not have to be remade when the magnitude of the
inputs to the FFT change).

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?

Any questions, mail me or post...

Thanks all,
DAN

Dan Shimizu               shimizu@unix.sri.com