Design of Variable Fractional-Delay 2-D FIR Digital Filters by Weighted Least-Squares Approach

In the paper, the desired response of a variable fractional-delay (VFD) 2-D digital filter is analyzed in detail, and it is found that there are four types of 2-D symmetric/antisymmetric sequences need to be used for the design of VFD 2-D FIR digital filters. Moreover, due to the orthogonality among the approach functions, the four types of 2-D sequences can be determined independently, such that the dimension for each computation can be reduced drasticcally. For simplicity, only the design of odd-odd order VFD 2-D filters are presented in the paper, and the other cases can be achieved in the same manner. To reveal the coefficient characters, the symmetric/antisymmetric properties of filter coefficients and the relationships between coefficients all are tabulated. Also, a design example of nonseparable diamond-shaped low-pass VFD filter is presented to demonstrate the effectiveness of the proposed method.