Fast calculation of the coefficients of the generalized McClellan transform in 2-D FIR filter design

An approach for the evaluation of the coefficients of the generalized McClellan transform is presented in order to design 2-D finite impulse response (FIR) filters with arbitrarily shaped frequency responses. Two classes of transforms which fit to the design of quadrantally symmetric filters and that of general centro-symmetric filters, respectively, are investigated. An analytical solution for the transform coefficients is derived by formulating a least-square approximation problem for the designed transform. This solution permits fast calculation of the coefficients in terms of the expected contour mapping requirements for the designed 2-D filter. In this method, the transform coefficients can be approximately scaled without requiring an optimization procedure