From: utzoo!decvax!pur-ee!malcolm
Newsgroups: net.math
Title: Interpolation of Complex Numbers - (nf)
Article-I.D.: pur-ee.524
Posted: Mon Sep  6 01:26:49 1982
Received: Mon Sep  6 06:34:54 1982

#N:pur-ee:6600005:000:1109
pur-ee!malcolm    Sep  5 14:08:00 1982

I had excellent luck the last time I submitted one of my research problems
to the network, so I am going to try again.  Part of the problem is that
I am not sure the best way to pose the problem....please bear with me.
If anybody has seen a problem of this type or knows of any references.

I am doing work on Ultrasonic Diffraction Tomagraphy and we have to 
interpolate complex numbers.  The actual interpolation is easy and
is well described by a number of books.  The problem is do we represent
the complex numbers in rectangular form or in polar form.  Consider the
numbers 0+j1 and 0-j1.  In rectangular form this averages to 0, while
in polar form they become mag=1, phase=90 and mag=1, phase=-90 and they
average to +1.  The results are quite different.

Since we are using the interpolation to supply numbers for an FFT algorithm
my inclination is to say that the rectangular form should be used.  I
can't even begin to justify my choice though.

How about it net-land???  Does anybody have any ideas??

					Malcolm Slaney
					Purdue EE Dept.
					{decvax,harpo,ihnss,ucbvax}
						!pur-ee!malcolm