Generalized time-frequency distributions and applications

Abstract A decomposition of the derivatives of or-der of a polynomial φ(t) is proposed in terms of φ(t − t0),..., φ(t − tn). This result allows us to intro-duce generalized time-frequency distributions for study-ing polynomial phase signals with constant amplitude in order to determine the degree and the coefficients of the corresponding phase. Relationships between these distributions and the already known polynomial distri-butions are established. Statistical properties of the proposed distributions are studied and their application for estimating the instantaneous frequencies in multiple chirp signals are discussed.