Optimisation of windowing for harmonic recovery in large-amplitude Fourier transformed a.c. voltammetry

The Fourier transform (FT)/band filtering (windowing)/inverse Fourier transform (iFT) sequence of operations with rectangular or 'bell-shaped' window functions is widely used for signal processing in physical chemistry and, in particular, in the technique of FT a.c. voltammetry (FTACV). However, the use of the rectangular window introduces 'ringing noise' (oscillations) into the iFT data, which may mask the faradaic a.c. signal of interest in the higher order harmonics that are available in large amplitude FTACV, while 'bell-shaped' functions may distort the magnitude and shape of the recovered a.c. harmonic components. The application of a new adjustable hybrid window based on the convolution of a rectangular and a Gaussian profile is now introduced to diminish the magnitude of the 'ringing'. The use of such a window is shown to significantly reduce both the amplitude and propagation time of the 'ringing' and, at the same time preserves the magnitude and shape of the recovered harmonic components. These attributes facilitate the accurate recovery of the faradaic signal. The advantages provided by application of the hybrid window when estimating thermodynamic and kinetic parameters from optimised comparisons of experimental and theoretical FTACV data are demonstrated.