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 Complex Exponentials
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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 counter-clockwise 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?
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Location: Germany
Quote:
 I don't know how to plot a function in this form:
Quote:
 In this case the complex exponential represents a sine wave. Plotted on a polar graph it is a vector that rotates counter-clockwise at a rate of w radians per second. The frequency is w/2 Pi. t is time.
It´s a rotating pointer that has an amplitude of 1.
It starts in the direction of the "real"-axis and represents a sine-wave.
wikipedia
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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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