Design of complex FIR filters with arbitrary complex frequency responses by two real Chebyshev approximations

The well-known Parks-McClellan program can only design linear phase real FIR filters, and the Remez exchange algorithm is not readily applied for general complex FIR filter design. Here the problem of designing complex FIR filters is solved by dividing the original complex approximation into two real ones such that the Remez exchange algorithm can be applied by slightly modifying the Parks-McClellan-McCalling program. Arbitrary frequency response complex FIR filters and complex all-pass filters can be easily designed by this efficient technique. This approach has several practical advantages such as fast design time and easy implementation with satisfactory performance.