Abstract
An extension of a polynomial consists of the polynomial plus higher power terms. Given a polynomial with real coefficients and an integer larger than its degree, a method is given that produces a finite list of extensions of degree this larger integer such that this list necessarily contains the extension whose largest root is as small as possible. This extension is called the pole radius minimizer. The pole radius minimizer is then found by the finite check of comparing the polynomials in the list. The method is applied to obtain filter transformations that are optimal as regards throughput, but also have considerable savings in hardware overhead compared with standard methods such as Scattered Lookahead and Minimum Order Augmentation. The table in Section 5 gives an explicit comparison for various kinds of filters.
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