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.
