From: utzoo!decvax!pur-ee!malcolm Newsgroups: net.math Title: Re: Interpolation of Complex Numbers - (nf) Article-I.D.: pur-ee.542 Posted: Sun Sep 12 22:27:26 1982 Received: Mon Sep 13 02:15:44 1982 #R:pur-ee:6600005:pur-ee:6600007:000:2026 pur-ee!malcolm Sep 12 20:15:00 1982 I sort of blew it. In my original letter of 9/5 I described the process of interpolating complex numbers by showing the "average" of two numbers in both rectangular and polar forms. A large number of people (cbosgd!djb, psuvax!sibley, houti!kdh, burdvax!puder, utcsrgv!wessels, tekcad!franka) were good enough to point out that my calculations of the average of two complex numbers when expressed in polar forms was incorrect. The key to this (as pointed out by houti!kdh) is that a vector operation ALWAYS has the same physical result, no matter what the representation. Tim Grogan (pur-ee!grogan) suggested a better example to illustrate my problem. Consider a simple exponential function of the form j*PI*t y(t) = e If this function is known for integer values of t then it makes perfect sense to consider this function to have magnitude equal to 1 and a phase of (j*PI*t). This was the type of function that I was alluding to in my previous letter. If the value of the function is known at times 0, y(0) = 1+j0, and t=1, y(1) = -1+j0, then the best approximation to y(.5) is not found from simply averaging the two vectors in rectangular form but from considering the magnitude and phase seperately. In this case the magnitude is always equal to 1, but the phase is a linear function of time. The "polar interpolate" at t=.5 is therefore magnitude=1 and phase=PI/2, or 0+j1. So my problem still remains. It is not simply a matter of vector arithmetic as I first thought, but a matter of choosing an appropiate interpolating function. Does anybody have any ideas on how I can decide whether I should use a rectangular coordinate system or a polar form when I do the interpolation? My data represents complex amplitude of a waveform and I need to interpolate the measured values onto a uniform grid so that I can do further computations on the matrix. So if anybody has any ideas, please mail me a note. Malcolm Slaney Purdue EE Dept. {decvax,harpo,ihnss,ucbvax,gsp86}! malcolm