Generalized time-frequency distributions and applications

A decomposition of the derivatives of order — of a polynomial φ(t) is proposed in terms of φ(t − t0),…, φ(t − tn). This result allows us to introduce generalized time-frequency distributions for studying 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 distributions are established. Statistical properties of the proposed distributions are studied and their application for estimating the instantaneous frequencies in multiple chirp signals are discussed.