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The computational cost for the design of FIR digital filters with short or medium length impulse responses is insignificant. However, the computational cost of conventional FIR filter design programs is , where denotes the length of the impulse response. Several hours of CPU time may be required to compute the coefficients in a very long filter, as for example in the case of . Here we discuss an improved method which can significantly reduce the computational requirements for the design of very long FIR digital filters.