A real-time implementable subclass of quadratic time-frequency representations

One of the major obstacles for quadratic time-frequency representations to be used in real (finite)-time applications is the computational complexity. In this paper, a real (finite)-time implementable subclass of Cohen´s (1966) class of distributions (CCD) is defined using windowing techniques. The kernel function for each member in this subclass can be characterized by a necessary and sufficient real(finite)-time implementable condition (RTIC) imposed on “global” kernels and “local” kernels in the ambiguity function domain. By choosing special “local” kernels, one can obtain the spectrogram (SPG) and the pseudo-Wigner-Ville distribution (PWVD) as special cases of this subclass. Our results show that time-frequency representations suitable for real-time implementation can be obtained that provide better resolution tradeoff between the time and frequency domains than occurs with the SPG and better frequency interference than occurs with the PWVD