Simultaneous wavelet and spline smoothing of noisy data

Two data smoothing algorithms using wavelet transforms are proposed. These algorithms take advantage of the time and frequency localization capabilities of wavelets. The first, a finite impulse response (FIR) filtering algorithm, allows real-time smoothing of selected time epochs within each frequency band. The second, a wavelet-based generalized cross validation (GCV) algorithm, provides potentially more optimal smoothing than standard GCV algorithms by allowing for individual smoothing parameters for each frequency band, as opposed to a single smoothing parameter for the overall signal.<>