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
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
You gave the answer yourself:I don't know how to plot a function in this form:
It´s a rotating pointer that has an amplitude of 1.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 starts in the direction of the "real"-axis and represents a sine-wave.
wikipedia
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