A class of low-noise computationally efficient recursive digital filters with applications to sampling rate alterations

Abstract

A new structure for multiband recursive digital filters is proposed. For meeting low-pass filter specifications, it uses fewer multiplications than conventional elliptic filter realizations. An approximation to the minimax solution is obtained numerically by minimizing the LP error norm. The analytic optimum for odd order low-pass filters of this new class turns out to be the elliptic filter itself, but in a new configuration. Analytic solution is also obtained for filters used in decimation/interpolation by a factor of 2. There are several realizations for this new structure, the choice of which depends on the location of poles and zeros. Some selected realizations always have low roundoff noise and small limit cycle bounds.