Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Computationally Efficient Scale Covariant Time-Frequency Distributions Selin Aviyente | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 204351 6 pages doi 2009 204351 Research Article Computationally Efficient Scale Covariant Time-Frequency Distributions Selin Aviyente Department of Electrical and Computer Engineering Michigan State University East Lansing MI 48824 USA Correspondence should be addressed to Selin Aviyente aviyente@ Received 3 October 2008 Revised 14 January 2009 Accepted 3 February 2009 Recommended by Ulrich Heute Scale is a physical attribute of a signal which occurs in many natural settings. Time-frequency distributions TFDs belonging to Cohen s class are invariant to time and frequency shifts but are not necessarily covariant to the time scalings of the signal. Conditions on the time-frequency kernel for yielding a scale covariant distribution have been previously derived Cohen 1995 . In this paper a new class of computationally efficient scale covariant distributions is introduced. These distributions are constructed using the eigendecomposition of time-frequency kernels Burrus et al. 1997 . The performance of this new class of distributions is illustrated with examples and is compared to conventional scale covariant distributions. Copyright 2009 Selin Aviyente. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Scale is a physical attribute of signals just like frequency. Self-scaling of signals is a phenomenon that is observed in different natural settings including biological and acoustic signals. Time-frequency distributions are designed to represent the energy distribution of nonstationary signals simultaneously in time and frequency but do not necessarily reflect the changes in scale. A bilinear continuous timefrequency distribution TFD belonging to Cohen s class is represented as
