A new method of designing FIR digital filters using nonuniform frequency samples is presented. There is no restriction on the phase to be linear. The method is based on a Newton-type polynomial interpolating on the unit circle of the complex plane. Attractive features of the proposed method are the applicability to unequally spaced samples, the recursive and semipermanent computation of filter parameters, the capability of obtaining short transition bands or sharp cut-off frequency responses, and the design of efficient algorithms for real-time applications. In the serial case, when the next sample appears, the design parameters are evaluated only by updating the old ones with correction terms that could be used as indicators for convergence, approximation, or filter reduction. The method can be extended to m-D filter design, DFT calculation, design of parallel algorithms, etc.