Calculating scaling function coefficients from system response data for new discrete wavelet families

In this paper, a formula derived from the wavelet dilation equation is presented as a means to calculate scaling function coefficient values for arbitrary waveforms. The performance of this formula is assessed by analyzing the scaling functions of multiple Daubechies wavelets. With the goal of developing new discrete wavelet families that possess the characteristics of a specific system, the formula is applied to analytical and experimental response data. The relationship between the number of coefficients and their ability to successfully capture the features of the signal is studied. Further, a technique is developed for determining the requisite number of coefficients when applying the formula. This formula may serve as the foundation for the development of new families of discrete wavelets which can be based on the nominal characteristics of a given system for use in signal processing and model discretization applications.

► Development of method for calculating coefficients from arbitrary impulse response signals.
► Signal reconstruction accuracy studied versus the number of coefficients.
► Number of coefficients required for accurate reconstruction increase with signal complexity.