Weighted median filters: generation and properties

It is shown, without reference to threshold decomposition or stacking property, that a WM (weighted median) filter of size N, with discrete-time continuous-valued inputs, can be specified by 2^N-1 mutually consistent linear inequalities relating the weights. The filter´s relation to binary threshold functions is indicated. For WM filters with symmetric weights, it is shown that the specification is the same as for ternary threshold functions. On the basis of the inequalities specifying a WM filter, some deterministic properties are derived and the generation of the WM filter is discussed