Wavelet transform-based Fourier deconvolution for resolving oscillographic signals

Fourier self-deconvolution is an effective means of resolving overlapped bands, but this method requires a mathematical model to yield deconvolution and it is quite sensitive to noises in unresolved bands. Wavelet transform is a technique for noise reduction and deterministic feature capturing because its time-frequency localization or scale is not the same in the entire time-frequency domain. In this work, wavelet transform-based Fourier deconvolution was proposed, in which a discrete approximation (such as A(2)) obtained from performing wavelet transform on the original data was substituted for the original data to be deconvolved and another discrete appropriate approximation (such as A(5)) was used as a lineshape function to yield deconvolution. Again, instead of the apodization function, the B-spline wavelet was used to smooth the deconvolved data to enhance the signal-to-noise ratio. As a consequence, this method does not suffer as badly as Fourier self-deconvolution from noises in the original data. Thus, resolution enhancement can be increased significantly, especially for signals with higher noise level. Furthermore, this method does not require a mathematical model to yield deconvolution; it is very convenient to deconvolve electrochemical signals.