The application of the wavelet power spectrum to detect and estimate 1/f noise in the presence of analytical signals Original Research Article

The wavelet power spectral density is a low-resolution equivalent to the traditional power spectral density based on the Fourier transform. The time information obtained by the wavelet transform is utilized to eliminate high frequency components of the analytical signal that would interfere with the analysis of the baseline noise. The median absolute deviation is used as a robust estimator of the standard deviation, because it is not affected by the aforementioned problems. In the case of a mixed random process, consisting of a first-order auto-regressive random process and additive white noise, the ability of the F-test to detect the presence of correlated noise depends on the length of the signal and the ratio of the variances of both noise components. The exponent of 1/f noise is estimated by weighted least squares. Signals from flow injection analysis demonstrate how the method can be applied to time varying systems.