Analysis of discretization errors in if estimation of polynomial phase signals

The peak of the polynomial Wigner-Ville distribution (PWVD) is a method for providing an unbiased estimate of the instantaneous frequency (IF) for polynomial phase signals. The theoretical lower variance bound, assuming a continuous frequency variable, has been studied previously in [1]. However, due to the discretization of the PWVD required for computer implementation, there is also another theoretical lower variance bound which is a result of the discretization error. In this paper, we study the relationship between the discretization error bound and the theoretical lower variance bound and determine the minimum number of frequency samples required such that the theoretical lower variance bound can be attained.