I have a signal: $f_i(t_i=i\Delta t)$, where $i = 0\ldots n-1$.
The signal seems to vary quickly around a slower varying "trend". I am assuming that the quickly varying part is noise and the slowly varying part is the real signal.
How do I estimate the signal-to-noise ratio (SNR) of the signal?
I guess that if I could decide on a treshold frequency: $\omega_t$ I could use the following expression:
$$S/N=\frac{\displaystyle\int_0^{\omega_t}|F(\omega)|^2}{\displaystyle\int_{\omega_t}^{\infty}|F(\omega)|^2}$$ where $F$ denotes the Fourier transform of $f(t)$.