A transform adapted to polynomial phase signals

We deal with signals of the form A exp(i/spl Sigma//sub k/=0/sup p/a/sub k/t/sup k/)+b(t) where b(t) is a Gaussian white noise. In order to estimate the highest order coefficient a/sub p/, we define a Fourier transform adapted to polynomial phase signals (PPS) with a given degree. The notion of polynomial translation in a quotient space of the field of complex numbers allows the introduction of a theoretical framework in which the classical tools of the signal processing-like convolution and filtering-can be redefined.<>