The application of frequency-weighting to improve filtering and smoothing performance

Pioneering research on the perception of sounds at different frequencies was conducted by Fletcher and Munson in the 1930s. Their work led to a standard way of weighting measured sound levels within investigations of industrial noise and hearing loss. Frequency weightings have since been used within filter and controller designs to manage performance within bands of interest. This paper introduces iterative frequency weighted filtering and smoothing procedures. It is assumed that filter and smoother estimation errors are generated by a first-order moving-average (AR1) system. This AR1 system is identified and used to apply a frequency weighting function within the design of minimum-variance filters and smoothers. It is shown under prescribed conditions that the described solutions result in nonincreasing error variances. An example is described which demonstrates improved mean-square-error performance.