A simple scheme for adapting time-frequency representations

Signal-dependent time-frequency representations, in which the kernel or window adapts to the signal being analyzed, perform much better than traditional time-frequency representations for many types of signals. Current signal-dependent time-frequency representations are blockoriented methods suited only for short-duration signals, and many are quite expensive computationally. We propose here a simple, computationally efficient technique for creating adaptive time-frequency representations, in which a kernel characterized by one free parameter is adapted over time. Time adaptation of the kernel allows continuous updating of the kernel to optimally track changes in signal characteristics. The procedure computes a short-time quality measure (concentration or entropy based) of the timefrequency representation for a range of values of the free parameter, and estimates the parameter value maximizing the quality measure via interpolation. Many representations, such as short-time Fourier transforms, cone-kernel distributions, or continuous wavelet transforms, can easily be made adaptive, with a computational cost of the same order as the fixed-kernel representations. Simple examples illustrate the benefits of this technique over fixed-kernel representations.