SIGNAL-DEPENDENT TIME-FREQUENCY ANALYSIS USING A RADIALLY GAUSSIAN KERNEL

Time-frequency distributions are two-dimensional functions that indica te the time-varying frequency content of one-dimensional signals. Each bilinear time-frequency distribution corresponds to a kernel function that controls its cross-component suppression properties. Current dis tributions rely on fixed kernels, which limit the class of signals for which a given distribution performs well. In this paper, we propose a signal-dependent kernel that changes shape for each signal to offer i mproved time-frequency representation for a large class of signals. Th e kernel design procedure is based on quantitative optimization criter ia and two-dimensional functions that are Gaussian along radial profil es. We develop an efficient scheme based on Newton's algorithm for fin ding the optimal kernel; the cost of computing the signal-dependent ti me-frequency distribution is close to that of fixed-kernel methods. Ex amples using both synthetic and real-world multi-component signals dem onstrate the effectiveness of the signal-dependent approach - even in the presence of substantial additive noise. An attractive feature of t his technique is the ease with which application-specific knowledge ca n be incorporated into the kernel design procedure.