Rank order processors for robust bandpass filtering

It is difficult for linear filters to enhance or preserve sharp edges and suppress the noise at the same time, because their application is based on spectral separation. Linear filters result in blurring edges. Moreover, linear filtering techniques designed under additive Gaussian noise assumption may suffer significant degradation when the actual noise statistics deviate from the assumed model, e.g., under impulsive noise environments. It is well-known that for such situations non-linear filtering techniques such as median filtering may be more effective.A rank order processor (ROP) is a non-linear signal processor with each output value causally related to the input values via a lattice polynomial. Median filters and rank-order filters are included in this class of processors.In the dissertation, we investigate an elaborated version of ROPs in terms of the following: (i) a design procedure, (ii) algorithms, (iii) root signals, and (iv) several interesting features including bandpass capability. With monotone commutativity, the theory of automata and regular sets facilitates the above analyses in that elaborated ROP operations in terms of real values can be reduced to ternary operations. This, along with the concept of root signals, leads to a novel design procedure in which designing a signal processor starts with a description in terms of regular sets.We observe that the elaborated ROPs proposed here have error correction capability and a bandpass effect. Using computer simulations, those features are examined for signals such as AM/FM signals, square waves, and speech-like signals. Simulation results confirm the robustness of the elaborated ROPs: (i) not optimal but reasonable suppression capability against Gaussian noise, (ii) excellent outlier rejection capability, and (iii) sharp edge passing capability. Since non-linear filtering operations generally cannot be characterized in frequency domain, elaborated ROPs having bandpass capability raise possibilities of new application areas for classes of signal processors requiring a robust bandpass feature.