
Home  Forums  Rules  Articles  diyAudio Store  Gallery  Wiki  Blogs  Register  Donations  FAQ  Calendar  Search  Today's Posts  Mark Forums Read  Search 
MultiWay Conventional loudspeakers with crossovers 

Please consider donating to help us continue to serve you.
Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving 

Thread Tools  Search this Thread 
27th December 2005, 05:11 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, 05:34 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, 06:45 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, 07:53 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, 10:15 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 
Thread Tools  Search this Thread 


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How complex to make an amplifier ? (lighthearted)  Bigun  Solid State  52  6th July 2009 10:39 PM 
Am I getting needlessly complex?  Mr Teal  MultiWay  1  24th January 2005 02:42 AM 
Passlabs Becomes Complex  A'af  Pass Labs  17  16th October 2003 04:22 PM 
Complex Emitter follower  Banfi T.  Solid State  104  1st April 2003 11:05 PM 
New To Site?  Need Help? 