How get amplitude and phase as a function of time?

1. May 1, 2014

Jhenrique

Given a function of the time like $f(t)$, its Fourier transform is $F(\nu)$ and by definition, $Abs(F(\nu))=A(\nu)$ and $Arg(F(\nu)) = \varphi(\nu)$, so I have amplitude and phase as function of the frequency, but make sense speak in amplitude and phase as function of the time? If yes? How get them?

2. May 1, 2014

MisterX

$\text{abs}(f(t))$ and $\text{arg}(f(t))$ of course

3. May 1, 2014

Jhenrique

But if f(t) = cos(t) thus the amplitude as function of the time is A(t) = 1 and the phase is φ(t) = 0 what is different of Abs(f(t)) and Arg(f(t)), respectively.

4. May 1, 2014

5. May 2, 2014

Jhenrique

argument is different of phase