FIR-median hybrid filters with predictive FIR substructures

A class of finite-impulse response (FIR) median hybrid (FMH) filters that contain linear FIR substructures to estimate the current signal value using forward and backward prediction is introduced. The output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window. Predictors maximizing the signal-to-noise ratio on signal sections described by an lth-order polynominal are derived. The ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the standard median (SM) filters. The new predictive FMH filters are shown to have root signals which do not exist for the SM filters, e.g. triangular waves. By combining the level and the ramp enhancement FMH filters, a filter is obtained which attenuates noise on constant and ramp signals. The noise attenuation on ramp signals is better than with the SM filter, and the predictive FMH filter has novel and meaningful root structures. The number of arithmetic operations needed to implement the predictive FMH filter grows linearly with the length of the filter