Median type filters with linear predictive substructures

In this paper, we introduce a new class of FIR Median Hybrid (FMH) filters which contain linear FIR substructures to estimate the current signal value using forward and backward prediction. 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 1th order polynomial 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, we obtain a filter which attenuates noise on constant and ramp signals.