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

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2 Author(s)
Tian-Bo Deng ; Dept. of Inf. Sci., Toho Univ., Chiba, Japan ; Wu-Sheng Lu

This paper proposes a closed-form weighted least-squares solution for designing variable two-dimensional (2-D) finite-impulse response (FIR) digital filters with continuously variable 2-D fractional delay responses. First, the coefficients of the variable 2-D transfer function are represented by using the polynomials of a pair of fractional delays (p1, p2). Then the weighted squared-error function of the variable 2-D frequency response is derived without sampling the two frequencies (ω1, ω2) and 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. Based on the error function, the closed-form optimal solutions for the coefficient matrices of the variable 2-D transfer function can be determined through solving a pair of matrix equations. In addition, Cholesky decomposition is applied to the final closed-form expressions in order to avoid some numerical instability problem. An example is given to illustrate the effectiveness of the proposed design method

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Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:47 ,  Issue: 2 )