Weighted least-squares method for designing variable fractionaldelay 2-D FIR digital filters

摘要

This paper proposes a closed-form weighted least-squares solutionnfor designing variable two-dimensional (2-D) finite-impulse responsen(FIR) digital filters with continuously variable 2-D fractional delaynresponses. First, the coefficients of the variable 2-D transfer functionnare represented by using the polynomials of a pair of fractional delaysn(p1, p2). Then the weighted squared-error functionnof the variable 2-D frequency response is derived without sampling thentwo frequencies (Ω1, Ω2) and twonfractional delays (p1, p2), which leads to ansignificant reduction in computational complexity. With the assumptionnthat the overall weighting function is separable and stepwise, thendesign problem is reduced to the minimization of the weightednsquared-error function. Based on the error function, the closed-formnoptimal solutions for the coefficient matrices of the variable 2-Dntransfer function can be determined through solving a pair of matrixnequations. In addition, Cholesky decomposition is applied to the finalnclosed-form expressions in order to avoid some numerical instabilitynproblem. An example is given to illustrate the effectiveness of thenproposed design method