To smooth a signal using wavelet smoothing, Origin first decomposes the signal into several sets of approximation coefficients and detail coefficients using multi-level 1-D wavelet decomposition. Then part of the detail coefficients are set to zeros. Finally, an inverse wavelet transform is carried out on the truncated detail coefficients and the approximation coefficients to gain the smoothed signal.
Multil-evel 1-D wavelet decomposition is a process of successively decomposing the approximation coefficients. The level determines how many times that the decomposition is performed. And in this function, it is calculated by ,
where N is the length of the input signal.
The wavelet decomposition and reconstruction used in this X-Function are implemented with NAG functions: nag_dwt() and nag_idwt().