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A new method is presented for representing and approximating signals which are made up of odd frequency components. The method uses a 'half-basis' set, all of whose members exhibit identical power spectral densities. In contrast to the con ventional Fourier approximation, approximations by this new method will spread the approximation error over the odd frequencies in the half basis. Approxima tions to the full set of signals, i.e. those containing both even and odd frequency components candoi:10.1098/rspa.1995.0047 fatcat:yfhjwgyewze6bh76vtqamdmqcu