Time-frequency distributions using rotated-window spectrograms

Previously proposed methods for combining multiple spectrograms with different length analysis windows have been shown to result in improved time-frequency distributions (TFD) for certain classes of signals. Such TFDs are purely positive and have time and frequency marginals which are closer to the "correct" signal marginals than any of the individual spectrograms. The marginals of such TFDs taken along directions not parallel to the time or frequency axes, however, are not improved. In this paper we extend the method of combining spectrograms to include spectrograms with "rotated windows" in which the resolution trade-offs can occur along any direction in the time frequency plane. The resultant new TFDs can have improved resolution and better agreement with the signal marginals along arbitrary directions in the time-frequency plane, not just parallel to the time and frequency axes.