Hilbert transform of voltammetric data

Abstract

The use of the fast Fourier transform (FFT) assumes stationarity and, in many applications, linearity; assumptions that are often invalid in the analysis of voltammetric data. Empirical mode decomposition followed by the Hilbert transform offers an alternative mode of analysis that can overcome these difficulties. The validity of the Hilbert transform for the analysis of non-linear signals merits application to electrochemistry which, to our knowledge, has not been carried out before. Preliminary results, for three well-characterised redox processes: (i) a thermodynamically reversible electron transfer; (ii) formation of a passivating layer; (iii) growth of an oxide layer on an electrode surface, suggest that it can provide useful and novel insights into electrochemical processes. A less well-characterised process, the adsorption of 5-hydroxytryptamine (5-HT) oxidation products on the surface of a glassy carbon electrode, is also investigated using the Hilbert transform.