Design of complex coefficient FIR digital filters using weighted approximation

Two theorems related to the Fourier transform of the complex time function are shown. By using these theorems and the Remes exchange algorithm, a minimax design method for complex-coefficient FIR (finite-impulse response) digital filters is proposed. The method reduces the complexity of the calculations, because the real and imaginary parts of the desired impulse response can be designed independently. It has been shown that this method attains sufficient accuracy in approximation both magnitude and phase (group delay) responses by design examples.<>