On establishing the bounds for binary scaled coefficients of fifth and seventh order polyphase half-band filters

This paper reports on establishing a good starting point for a half-band fixed-point polyphase filter design technique, which employs a natural algorithm, when fifth and seventh order filter structures are used. It should be noted that the convergence of combinatorial algorithms is sensitive to initial conditions implying that the seed filter coefficients and search space for subsequent filters need to be chosen with care for the algorithm to converge efficiently. This requires the definition of a bounded area and bounded volume in the coefficient space for the fifth and seventh order filters respectively. This will ensure that the zeroes are on the unit circle, and hence, will result in maximum null depths being achieved at the zero frequencies (as is the case with the elliptic approximation)