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Foreword.- Introduction.- Operators on Sequences.- Basic Rank Selectors, Pulses and Impulses.- LULU-Smoothers, Signals and Ambiguity.- LULU-Intervals and Similar Smoothers.- Smoothing and Approximation with Signals.- Variation Reduction and Shape Preservation.- Multiresolution Analysis of Sequences.- The Discrete Pulse Transform.- Fair Comparison with Linear Smoothers.- Interpretation and Future.- Bibliography.