Equiripple design in complex domain for FIR digital filters by transforming desired response

In this paper, a new design method is proposed for complex equiripple approximation of an FIR digital filter. In this method, the desired characteristics are varied and the least-squares method is applied iteratively until convergence to an equiripple solution is reached. Although the obtained solution is quasi-optimal, the necessary computational complexity is extremely small in each iteration and the computation error can be kept small. Therefore, the method has the advantage that the design of higher-order filters, which is difficult in the conventional methods, can now be executed at high speed. By computer simulation, the method is compared with the conventional complex Chebyshev approximation method and the effectiveness of the present method is demonstrated.