74. Applications of Non Orthogonal Filter Banks to Signal and Image Analysis
A non-orthogonal wavelet-based multiresolution analysis was already provided by scaling and wavelet filters derived from Gegenbauer polynomials. Allowing for odd n (the polynomial order) and a value (a polynomial parameter) within the orthogonality range of such polynomials, scaling and wavelet functions are generated by frequency selective FIR filters. These filters have compact support and generalized linear phase. Special cases of such filter banks include Haar, Legendre, and Chebyshev wavelets. As an improvement, it has been achieved that for specific a values it is possible to reach a filter with flat magnitude frequency response. We obtain a unique closed expression for a values for every n odd value. The main advantages in favor of Gegenbauer filters are their smaller computational effort and a constant group delay, as they are symmetric filters. Potential applications of such wavelets include fault analysis in transmission lines of power systems and image processing.