Discretization-free method for designing variable fractional delay 2-D FIR filters

This paper proposes a closed-form weighted least-squares solution for designing variable two-dimensional (2D) digital filters with continuously variable 2D fractional delays. First, the coefficients of the variable 2D FIR filter are represented by using the polynomials of a pair of fractional delays (p₁,p₂). Then the weighted squared-error function of the variable 2D frequency response is derived without sampling the two frequencies (w₁,w₂) and the two fractional delays (p₁ , p₂), which leads to a significant reduction in computational complexity. With the assumption that the overall weighting function is separable and stepwise, the design problem is reduced to the minimization of the weighted squared-error function. Finally, the closed-form solutions for the optimal coefficient matrices of the variable 2D FIR filter are derived