Least-square method for 2D FIR digital filters without matrix inversions

This paper proposes a least-square method (analytic least-square method) without a matrix inversion, to be applied to the 2D linear-phase FIR digital filter. The past analytic least-square method has a strong constraint that the characteristics should be specified for the whole frequency band. In this study, the orthonormal functions are defined for the 2D FIR filter, and new orthogonal functions are formed by applying the Gram-Schmidt orthogonalization. Then, an analytic least-square method is realized where the transition region is not included in the range of approximation. By this approach, the higher-order filters can be realized without computation error. Our approach also simplifies estimation of the least order, which is required to suppress the error within the tolerance.