Implementation of Digital Unbiased FIR Filters with Polynomial Impulse Responses

This paper addresses the design and implementation of digital unbiased finite impulse response (FIR) filters with polynomial impulse response functions. The transfer function, its fundamental properties, and a general block-diagram are discussed for the impulse response represented with the l-degree Taylor series expansion. As a particular results, we show a fundamental identity uniquely featured to such filters in the transform domain. For low-degree impulse responses, the transfer functions are found in simple closed forms and represented in compact block-diagrams. The magnitude and phase responses are also analyzed along with the group delays. A comparison with predictive FIR filters is given. As examples of applications, filtering of time errors of local clocks is discussed along with the low-pass filter design employing a cascade of the unbiased FIR filters.