# How to estimate the signal-to-noise ratio of a waveform?

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 $f(t)$.

• Could you post a periodogram? – user42 Dec 19 '11 at 15:46
• What are the characteristics of the noise? White/colored? Known distribution? Zero-mean? – Jason R Dec 19 '11 at 16:48