Combined Wavelet Transform with Curve-fitting for Objective Optimization of the Parameters in Fourier Self-deconvolution

Fourier self-deconvolution was the most effective technique in resolving overlapping bands, in which deconvolution function results in deconvolution and apodization smoothes the magnified noise. Yet, the choice of the original half-width of each component and breaking point for truncation is often very subjective. In this paper, the method of combined wavelet transform with curve fitting was described with the advantages of an enhancement of signal to noise ratio as well as the improved fitting condition, and was applied to objective optimization of the original half-widths of components in unresolved bands for Fourier self-deconvolution. Again, a noise was separated from a noisy signal by wavelet transform, therefore, the breaking point of apodization function can be determined directly in frequency domain. Accordingly, some artifacts in Fourier self-deconvolution were minimized significantly.