Complex Exponentials - diyAudio
Go Back   Home > Forums > Loudspeakers > Multi-Way

Multi-Way 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
Reply
 
Thread Tools Search this Thread
Old 27th December 2005, 04:11 AM   #1
diyAudio Member
 
Join Date: Oct 2005
Default 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
  Reply With Quote
Old 27th December 2005, 04:34 AM   #2
poobah is offline poobah  United States
diyAudio Member
 
poobah's Avatar
 
Join Date: Nov 2005
Hmmmm...

Use w (omega) as your "x" axis... should be a decaying sinusoid...

Is this what you are asking?
  Reply With Quote
Old 27th December 2005, 05:45 AM   #3
omba is offline omba  Japan
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?
  Reply With Quote
Old 27th December 2005, 06:53 AM   #4
joensd is offline joensd  Germany
diyAudio Member
 
Join Date: Dec 2001
Location: Germany
Quote:
I don't know how to plot a function in this form:
You gave the answer yourself:
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.
Its a rotating pointer that has an amplitude of 1.
It starts in the direction of the "real"-axis and represents a sine-wave.
wikipedia
__________________
jens
  Reply With Quote
Old 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
  Reply With Quote

Reply


Hide this!Advertise here!
Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off


Similar Threads
Thread Thread Starter Forum Replies Last Post
How complex to make an amplifier ? (lighthearted) Bigun Solid State 52 6th July 2009 09:39 PM
Am I getting needlessly complex? Mr Teal Multi-Way 1 24th January 2005 01:42 AM
Passlabs Becomes Complex A'af Pass Labs 17 16th October 2003 03:22 PM
Complex Emitter follower Banfi T. Solid State 104 1st April 2003 10:05 PM


New To Site? Need Help?

All times are GMT. The time now is 01:16 AM.


vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2014 DragonByte Technologies Ltd.
Copyright 1999-2014 diyAudio

Content Relevant URLs by vBSEO 3.3.2