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27th December 2005, 04:11 AM  #1 
diyAudio Member
Join Date: Oct 2005

Complex Exponentials
I got Dr. Earl Geddes and Lidia Lee's book, "Audio Transducers" for christmas and I am already stuck on page 1. The topic is complex exponentials.
A complex exponential is an exponential raised to a complex power: e^iwt where: e^iz = cos(z)+i sin(z) In this case the complex exponential represents a sine wave. Plotted on a polar graph it is a vector that rotates counterclockwise at a rate of w radians per second. The frequency is w/2 Pi. t is time. The thing that confuses me here is that the complex numbers that I am familiar with are in this form: a + bi = r [cos (theta) + sin (theta)] where: r = (a^2 + b^2)^0.5 Theta is the angle of interest on a polar plot, and r is the magnitude of the vector. I don't know how to plot a function in this form: e^iwt Can anyone help? Travis 
27th December 2005, 04:34 AM  #2 
diyAudio Member
Join Date: Nov 2005

Hmmmm...
Use w (omega) as your "x" axis... should be a decaying sinusoid... Is this what you are asking? 
27th December 2005, 05:45 AM  #3 
diyAudio Member
Join Date: Aug 2003
Location: Japan

e^iwt = e^i(wt)
so, wt = theta in your expression a+bi = r(cos(wt) + i*sin(wt)) Will this help? 
27th December 2005, 06:53 AM  #4  
diyAudio Member
Join Date: Dec 2001
Location: Germany

Quote:
Quote:
It starts in the direction of the "real"axis and represents a sinewave. wikipedia
__________________
jens 

28th December 2005, 09:15 PM  #5 
diyAudio Member
Join Date: Oct 2005

Thanks everyone for the help. I made a short program to plot this function in time based on your advice. It works just as the book says, a vector rotating at omega radians/sec .
Thanks again, Travis 
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