FIR Low-pass Digital Filters Research Articles

A novel algorithm for marine strapdown gyrocompass based on digital filter

With the rapid development of strapdown gyrocompass, few corresponding strapdown algorithms occur in publications, so that we have to use the conventional one designed for platform gyrocompass. Enlightened by IXSEA ideals, we proposed a novel algorithm which is suitable for marine strapdown gyrocompass. In our proposed algorithm, gyro outputs are used to track the body frame rotation, and the observation of the pure gravity slow drift in the inertial gives the navigation frame rotation. We also separate the pure gravity from interferential accelerations with a FIR low-pass digital filter. The analysis and numerical results show the better performance of the proposed algorithm than the conventional one.

Solving the Selesnick–Burrus filter design equations using computational algebra and algebraic geometry

In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters K, L, M. In certain cases (their “Region I”), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases (“Region II”), they proposed using Gröbner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick–Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved.