Re: fourier transform
The phase of the Fourier transform arises when you want to express the Fourier transform of a function in terms of a magnitude and phase, which are functions of frequency. Now, the meaning of the phase depends on the application you are working, mathematically it is the angle of a complex number. The phase can take values greater than 2*pi, then care should be taken when the fft is applied.
I guess somebody was referring to the Euler formula instead of "Eigen vector" in a previous post. The Fourier transform of cos(wo*t + c) = exp(i*c)*pi*Dirac(w-wo)+exp(-i*c)*pi*Dirac(w+wo), you can find it expanding cos(wo*t+c)=cos(wo*t)cos(c)-sin(wo*t)sin(c). Now, if we are talking about magnitude and phase, the magnitude introduced by exp(i*c) = 1, but it introduces a phase offset = arctg(c). It should be noted that the first term has a positive offset and the second is negative.
cheers
Sal