Detecting noise in a time series

A numerical algorithm is presented for estimating whether, and roughly to what extent, a time series is noise corrupted. Using phase-randomized surrogates constructed from the original signal, metrics are defined which can be used to quantify the noise level. A saturation occurs in these metrics at signal to noise ratios (SNRs) of around 0 dB and below, and also at around 20 dB and above. In between these two regions there is a monotonic transition in the value of the metrics from one region to the other corresponding to changes in the SNR.