Nonlinear time-frequency distributions with multiplication-free kernels

In this paper we introduce and analyze the so called complex sign WVD (CS-WVD), defined as the Wigner-Ville distribution (WVD) where one of the two signals is substituted by its complex sign. The substitution provides a consistent simplification for the implementation on dedicated hardware. In particular, the number of multiplications is drastically reduced. In spite of the hard nonlinearity used in the CS-WVD, the new transform is still able to deal with multi-component chirp signals. In the paper we provide a statistical analysis of the introduced transformation, in the case of polynomial-phase signals embedded in additive white Gaussian noise. The theoretical analysis is compared to simulation results and to the Cramer-Rao lower bounds.