Complex Frequency - This is a concept that does not get used much in practice.
Most people work with constant amplitude sinusoids (the radians/sec part of complex frequency)
And don't deal with signals that have an exponential envelope coefficient ( the σ part)
"the general complex frequency, s, can be thought of in terms of its real and imaginary parts:
s = σ + jω
or in terms of its period and periodic decay rate:
s = T-1ejα.
The former is always the most appropriate way to use the complex frequency in a Laplace or Fourier transform, however the latter offers a bit more insight.
The imaginary part of s:
Im{s} = ω
is what you would normally think of as "frequency." It tells you how often the signal goes from positive to negative. The real part of s:
Re{s} = σ
is what you would normally think of as "decay rate." It tells you how quickly the amplitude of the oscillations change."
from:
http://www.physicsforums.com/showthread.php?t=37945Above is a pretty good explanation. Wikipedia could use a good write-up on this one.