DESIGN AND PERFORMANCE OF COMBINATION FILTERS FOR SIGNAL RESTORATION

A class of nonlinear moving window filters is investigated for restoration of signals embedded in additive white Gaussian and non-Guassian noise. The filters of this class, which we call combination filters (C-filters), use both rank-order and temporal-order information from the input observation sequence within finite processing windows to produce the outputs. A C-filter combines the characteristics of linear FIR filters and nonlinear filters of the order statistics type. The output of a C-filter in each processing window is defined to be the rank-order-dependent weighting of temporal-order data. The temporal order of the data needs to be retained for linear processing in order to effect predictable modifications of the spectral content of the observed sequence, while the rank-order information can be used to reduce the influence of non-Gaussian noise components and to retain edges and details. We consider both analytical and training procedures to design the C-filters. To get further improvement in overall performance, we extend the concept of C-filters and introduce a class of generalized C-filters (GC filters) which are shown to have desirable properties. Performance characteristics of C-and GC filters in signal restoration are considered through computer simulation. We show that in frequency selective restoration of nonstationary signal waveforms, considerable improvement in performance can be achieved with these filters over linear filters.