Signal processing algorithms in piecewise polynomial bases

Abstract

This thesis describes a development of Haar and Harmut``s fast transformation algorithm for the calculation of coefficients both piecewise-linear and piecewise-quadratic bases factors in digital signal processing (DSP). In the thesis, the fundamentals introduced reasons, which involve attention of expert to Haar and Harmut``s bases: 1. Reduction number of the factors necessary for approximation (with the set accuracy) in relation to the general number of binary pieces. 2. Absence of ``long`` operations in expression (1.3.4.). Operations of addition, subtraction and shift are used only. In the thesis, the results of the comparative analysis of possibilities piecewise-polynomial local bases on three parameters are shown: by quantity of indispensable operations, by efficiency of compression of the information and by error. Finally proposed achievement the advantages of piecewise-quadratic bases: greater accuracy and good smoothness of approximation in comparison with piecewise-constant and piecewise-linear bases.