Optimizing Time and Frequency Resolution for Detection and Classification

ABSTRACT. Research in time-frequency representations (TFRs) has often been directed towards determining how two-dimensional weighting kernels, which operate convolutionally on Wigner-Ville distributions, effect desired properties and trade-offs of the resulting representation. For example, a kernel with a diamond-shaped support region results in a spectrogram which has the well-known trade-off between time and frequency resolution. Much past research has been directed at improving resolution, while ameliorating the quadratic interference of the Wigner-Ville approach. We take an entirely different view: Our final goal is data-trained pattern classification, where high resolution may only increase the need for training data. We thus change the standard approach to automatically determine the kernel which minimize the time and frequency resolution needed to differentiate multiple classes. The kernels are called “class-dependent kernels.” We have applied these class-dependent kernels to problems in multi-sensor helicopter fault diagnosis. In this application, perfect detection of the occurance of a fault and perfect classification of the type of fault was achieved. Also, the optimal sensors for each fault were automatically chosen.