The notions of time, frequency, and scale are generalized using concepts from unitary operator theory and applied to time-frequency analysis, in particular the wavelet and short-time Fourier transform orthonormal bases and Cohen's class of bi-linear time-frequency distributions. The result is an infinite number of new signal analysis and processing tools that are implemented simply by prewarpin...

This paper describes several approaches to analyzing the frequency, or pitch, content of the sounds produced by musical instruments. The classic method, using Fourier analysis, identifies fundamentals and overtones of individual notes. A second method, using spectrograms, analyzes the changes in fundamentals and overtones over time as several notes are played. Spectrograms produce a time-freque...

|We extend the characteristic function method (CFM) to more general groups, operators, and signal spaces. We show that the extended CFM can be applied to projected unitary operators as well as discrete-time/periodic signals.

We describe several aspects of wavelet analysis and more general methods of time-frequency analysis, emphasizing applications to signal analysis and processing problems.

In this paper we consider the construction of multiresolution Gabor dictionaries appropriate for audio signal analysis. Motivated by a desire for parsimony and efficiency, we propose and formalise the idea of reduced multi-Gabor systems, showing that they constitute a frame for L2(R) and other Hilbert spaces of interest. In order to demonstrate the practicality of such a scheme, we apply it to ...

Vibration problems in rotors can be extremely frustrating and may lead to greatly reduced reliability. By utilizing the proper data collection and analysis techniques, the faults because of vibration can be discovered and predicted. The signal analysis is important in extracting fault characteristics in fault diagnosis of machinery. The traditional signal analysis can not settle for non-station...