Time-frequency distributions based on generalized cone-shaped kernels for the representation of nonstationary signals

A generalized category of cone-shaped kernels is proposed. Analysis of the kernel in the 2-D time, 2-D frequency, and ambiguity domains is performed. The shape of this kernel in the 2-D time plane is bow-tie, which effectively suppresses cross-terms especially in the frequency direction. In the 2-D frequency plane, the shape of the kernel is of a lateral inhibition form, which enhances spectral peaks when convolved with the instantaneous spectral correlation. By investigating the new kernel in the ambiguity domain, it is shown that the resulting distribution has many desirable properties that encourage its use as a time-frequency signal analysis tool. By proper selection of kernel parameters, a family of kernels is obtained, hence, providing many kernels which may be used in the analysis of different types of signals, the most important of which are the Born-Jordan and ZAM (Zhao, Atlas and Marks) kernels. Experimental results on a simulated test signal that represents two short-duration Gaussian pulses show the advantage of the proposed distribution in comparison with ZAM and Born-Jordan distributions.