Choosing discrete orthogonal wavelets for signal analysis and approximation

The discrete wavelet transform decomposes a discrete time signal into an approximation sequence and a detailed sequence at each level of resolution. The approximation at any resolution is the projection of the signal onto the orthogonal space spanned by the translates of an analyzing scaling function. The choice of scaling function can have a large impact on the error in the approximation at a given resolution. A systematic method for generating scaling functions is developed. This method ensures that a scaling function will be found that is close to the optimum. The resulting scaling functions can be used by themselves or serve as starting point for further optimization.<>