Complex approximation of 2-D digital filters with prescribed log magnitude phase response

We propose a new design algorithm for nearly linear phase 2-D IIR (FIR) digital filters with prescribed log magnitude response. The error function used is the sum of the weighted log magnitude-squared error and phase-squared error, and so it is possible to control log magnitude and phase response independently. The gradient vector of the proposed error function is easily calculated as the closed form solution because of the nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples