the frequency of the " exponential " , (e) function

[hitman1988]

Hi all
we all know the exponential function (e) and we know it is aperiodic signal for infinitely time , does that mean it has no frequency i.e it's frequency is zero ?
that will mean it's DC signal which it is not ? so what is the answer? Assuming it's exponent is real

 

[steve.hunch]

Just do a Fourier transform of exponent and you will get it spectrum. You cannot say that it has no frequency. You must remember that frequency and time domain represent the same signal and have the same amount of information. if you have infinite long signal in time, that means that it has infinite information in time, so the same must be in frequency. (dc signal has no change in time, so enough to know one point and you know the rest, in frequency it has only one frequency - 0Hz).
Just do the transform and you see that spectrum of exp(-t)*u(t) exist