Abstract
AbstractA time–frequency transform is a sesquilinear mapping from a suitable family of test functions to functions on the time–frequency plane. The goal is to quantify the energy present in the signal at any given time and frequency. The transform is further specified by imposing conditions such as those stemming from basic transformations of signals and those which an energy density should satisfy. We present a systematic study on how properties of a time–frequency transform are reflected in the associated evaluation at time–frequency origin, integral kernel and quantization and discuss some examples of time–frequency transforms.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
Reference26 articles.
1. Auger, F., Hlawatsch, F. (eds.): Time-Frequency Analysis. Concepts and Methods. Digital Signal and Image Processing. ISTE Ltd, 2008, p. 434
2. Boggiatto, P., Carypis, E., Alessandro, O.: Windowed-Wigner representations in the cohen class and uncertainty principles. J. Geom. Anal. 23(4), 1753–1779 (2012)
3. Boggiatto, P., De Donno, G., Oliaro, A.: Time-frequency representations of Wigner type and pseudo-differential operators. Trans. Am. Math. Soc. 362(9), 4955–4981 (2010)
4. Born, M., Jordan, P.: Zur Quantenmechanik. Zeitschrift für Physik A Hadrons and Nuclei 34(1), 858–888 (1925)
5. Claasen, T.A.C.M., Mecklenbräuker, W.F.: The Wigner distribution - a tool for time-frequency signal analysis III: Relations with other time-frequency signal transformations. Philips J. Res. 35, 372–389 (1980)
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献