Design of FIR filters and allpass phase equalizers with prescribed magnitude and phase responses by two real Chebyshev approximations

It is noted that, since the coefficients of an FIR (finite impulse response) filter with arbitrary complex-valued desired frequency responses are neither symmetric nor antisymmetric, the Remez exchange algorithm cannot be applied directly. It is shown that the problem can be solved by dividing the original complex approximation into two real ones such that the Remex exchange algorithm can be applied by slightly modifying the Park-McClellan program. This method is much easier than the currently existing methods using linear programming and the performance is satisfied. More importantly, the overall complex errors are also equiripple in the complex Chebyshev sense. This approach has several practical advantages such as fast design time and easy implementation with comparable accuracy. Numerical design examples including a lowpass filter and sine-delay FIR allpass phase equalizers are given to show the effectiveness of this approach