The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N). © 2007 Science in China Press.
CITATION STYLE
Liu, J., Xu, J., Ning, X., & Tian, R. (2007). A non-commutative time-frequency tomography. Chinese Science Bulletin. Springer Verlag. https://doi.org/10.1007/s11434-007-0367-x
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