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This paper introduces a new class of multilinear functions which can be used for analyzing a signal with time-varying frequency. The new class subsumes a number of existing functions, including the higher order ambiguity functions (HAFs), the polynomial Wigner-Ville distributions (PWVDs), and the higher order phase (HP) functions. As well as establishing a link between these existing functions, the new class provides a formalism which allows for the creation of useful new multilinear functions. A number of new functions are derived from the class.