Signal-dependent time-frequency analysis using a radially Gaussian kernel

Time-frequency distributions are two-dimensional functions that indicate 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 distributions 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 improved time-frequency representation for a large class of signals. The kernel design procedure is based on quantitative optimization criteria and two-dimensional functions that are Gaussian along radial profiles. We develop an efficient scheme based on Newton's algorithm for finding the optimal kernel; the cost of computing the signal-dependent time-frequency distribution is close to that of fixed-kernel methods. Examples using both synthetic and real-world multi-component signals demonstrate the effectiveness of the signal-dependent approach-even in the presence of substantial additive noise. An attractive feature of this technique is the ease with which application-specific knowledge can be incorporated into the kernel design procedure.