Radial Function Based Kernel Design for Time-Frequency Distributions

Abstract

A framework based on the $n$ -dimensional Fourier transform of a radially symmetric function is introduced to design kernels for Cohen time-frequency distributions. Under this framework, we derive a kernel formula which generalizes and unifies MargenauHill, BornJordan, and Bessel distributions, using a realization based on a n-dimensional radial delta function. The higher order radial kernels suppress more cross-term energy compared with existing lower order kernels, which is illustrated by the time-frequency analysis of atrial fibrillation from surface electro cardiogram data.