Design of third order wavelet filters over finite fields by using special binomials

This work is concerned on research of method for design of third order wavelet filters in finite fields by using special binomials. Finite field wavelets have many advantages in comparison with real or complex field wavelets. The main two of them are high rate data processing and lack of rounding error. However, the main disadvantage of finite field wavelets is high complexity of design based on using of polynomial properties and para-unitary matrixes over finite fields. The most known methods for design of finite filed wavelets utilize computing system based on Berlekamp algorithm or its modifications for polynomial expansion over finite field. We propose new method for design of third order wavelet filters over finite field. Presented method is based on using of special type binomials over those fields. We derived and proved analytical formulas for filter coefficient and demonstrated some examples.