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A design method for half-band filters

Earlier methods of design have used iterative approaches such as the well-known Parks-McClellan algorithm or some variant of linear programming. Here we give a direct method of design, using Chebyshev polynomials, which provides a reduction in design time over previous methods by about a factor of ten. The ideal equal-ripple response in both passband and stopband is not achieved exactly, but the error is extremely small and would normally be undetectable in practical realizations.