Application of wavelet transforms to experimental spectra: Smoothing, denoising, and data set compression

Various methods have been proposed for smoothing and denoising data sets, but a distinction is seldom made between the two procedures, Here, we distinguish between them in the signal domain and its transformed domain, Smoothing removes components (of the transformed signal) occurring in the high end of the transformed domain regardless of amplitude, Denoising removes small-amplitude components occurring ist the transformed domain regardless opposition. Methods for smoothing and denoising are presented which depend on the recently developed discrete wavelet (DW) transform technique, The DW smoothing and denoising methods are filtering techniques that are applied to the transformed data set, prior to hack-transforming it to the signal domain, These DW techniques are compared with other familiar methods of smoothing (Savitzky-Golay) and denoising through filtering (Fourier transform), Preparatory to improving experimental data sets, synthetic data sets, comprised of ideal functions to which a known amount of noise has been added, are examined. The filter cutoffs are systematically explored, and DW techniques are shown to be highly successful for data sets with great dynamic range, In the minority of cases, smoothing and denoising are nearly interchangeable, It is shown that DW smoothing compresses with the most predictable results, whereas DW denoising compresses with minimal distortion of the signal.