In this thesis, we first discuss multiresolution analysis and perfect reconstruction filter banks that can be used both for computing discrete wavelet transform and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Then systemized algebraic approach to construct orthonormal wavelet basis is proposed by combining 2 band perfect reconstruction filter bank with regularity constraint. It is shown that algebraic equation of finding filter bank coefficients can be represented as a single variable of filter length, and uniqueness of filter coefficients and nonsigularity of this equation is also proved.
Extension to biorthogonal case is considered, and the fact that both algebraic equations of getting orthogonal and biorthogonal filter banks satisfying reguarity constraint are identical for same filter length is presented.
