The well‐known FFT (Fast Fourier Transform) algorithm of Cooley and Tukey has found widespread application in the field of numerical Fourier transforms and related problems. Nevertheless, the FFT algorithm has to be treated with caution, because in order to avoid aliasing in the frequency domain, it is restricted to the transform of bandlimited functions. A new algorithm has been developed that still has the FFT characteristics, but that is no longer confined to bandlimited functions. The new algorithm has been tested in the case of MBRS (Molecular Beam Relaxation Spectroscopy) linear system analysis.