A transform adapted to polynomial phase signals

We deal with signals of the form A exp(iΣ_k=0^pa_kt^k)+b(t) where b(t) is a Gaussian white noise. In order to estimate the highest order coefficient a_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