Abstract
A new, simple analytic method for the design of digital half-band filters is derived; for that, we introduce a closed form of the ideal half-band transfer function and apply polynomial approximations to the non-rational part. For the maximally flat half-band filter, we can find a new form especially suited for an implementation without multipliers, often using less than half the number of adders compared with the direct form. Furthermore, half-band filters with nearly perfect Chebyshev approximation can be generated; in general, the ripple exceeds the optimum value by less than 1% and is approximately halved compared to the Kaiser-window method.
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