Spectral characterisation of ternary threshold functions

In this communication, the question of characterising a ternary threshold function by a few coefficients of its series expansion in terms of Chrestenson functions is examined. It is shown that an n-place ternary threshold function may be uniquely characterised by (n+2) coefficients; (n+1) of them correspond to particular elements of the Chrestenson spectrum of the function and the n+2nd is the summation over all magnitude-squared spectral elements.