Implementation of unbiased FIR filters with low-degree polynomial gains

We discuss implementation of the unbiased finite impulse response (FIR) filters. The transfer function and general block-diagram are presented for the l-degree polynomial FIR filter along with its fundamental properties in the z-transform domain. As a special results, we show a fundamental identity that is uniquely featured to such filters and can serve as an indicator of unbiasedness in filter design. For low-degree gains, the transfer function is represented in simple closed forms and compact block-diagrams. An example of applications is given for filtering of time errors in a crystal clock.