Summary: An efficient method is proposed for the design of finite-duration impulse response (FIR) digital filters with arbitrary log magnitude and phase responses. The method is based on an iterative weighted genetic algorithm (GA) approach to obtain a least-squares approximation to the given log magnitude function and the weighting function at each iteration is updated using the result of the previous iteration, which leads to the optimal approximation in the log Chebyshev sense. The method can be easily modified to approximate arbitrary log complex-valued frequency response such as complex FIR log filters. Several numerical design examples are shown to demonstrate the effectiveness of this proposed approach.