![]() This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. Math.In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. Lamouchi, H., Omri, S.: Quantitative uncertainty principles for the short time Fourier transform and the radar ambiguity function. 31(3), 594–599 (1990)īoggiatto, P., Carypis, E., Oliaro, A.: Cohen class of time–frequency representations and operators: boundedness and uncertainty principles. Lieb, E.H.: Integral bounds for radar ambiguity functions and Wigner distributions. Birkhäser, Boston (2000)įu, Y., Kähler, U., Cerejeiras, P.: The Balian-law theorem for the windowed quaternionic Fourier transform. Gröchening, K.: Foundation of Time–Frequency Analysis. Hitzer, E.M.S.: Quaternion Fourier transform on quaternion fields and generalizations. 2013, 10 (2013)īahri, M.: On two dimensional quaternion Wigner–Ville distribution. 64(2), 223–242 (2018)īahri, M., Ashino, R., Vaillancourt, R.: Convolution theorem for quaternion fourier transform: properties and applications. 423(1), 681–700 (2015)Ĭheng, D., Kou, K.I: Properties of quaternion Fourier transforms (2016), arXiv:1607.05100Ĭheng, D., Kou, K.I.: Plancherel theorem and quaternion Fourier transform for square integrable functions. 17(3), 497–517 (2007)Ĭhen, L.P., Kou, K.I., Liu, M.S.: Pitt’s inequality and the uncertainty principle associated with the quaternion Fourier transform. Hitzer, E.: Quaternion Fourier transform on quaternion fields and generalization. ![]() In: Procedings of AGACSE (2012)īahri, M., Ashino, R.: A Variation on uncertainty principle and Logarithmic uncertainty principle for continuous quaternion wavelet transforms. Bie, H.: New techniques for two-sided quaternion for two sided quaternion Fourier transform. 53(8), 3111–3128 (2005)īahri, M., Hitzer, E., Hayashi, A., Ashino, R.: An uncertainty principle for quaternion Fourier transform. ![]() Hahn, S.L.: Wigner distributions and ambiguity functions of 2-D quaternionic and monogenic signals. 216, 2366–2379 (2010)īahri, M., Saleh, M., Fatimah, A.: Relation between quaternion Fourier transform and quaternion Wigner–Ville distribution associated with linear canonical transform. 53(8), 3111–3128 (2005)īahri, M., Hitzer, E., Ashino, R., Vaillancourt, R.: Windowed Fourier transform of two-dimensional quaternionic signals. ![]() Hahn, S.L., Snopek, K.M.: Wigner distributions and ambiguity function of 2-D quaternionic and monogenic signals. (ed.) Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics, pp. Germany: Institut fur informatik and Prakttische Mathematik, University of Kiel (1999)īulow, T., Felsberg, M., Sommer, G.: Non-commutative hypercomplex Fourier transforms of multidimensional signals. ![]() 3(3), 207–238 (1989)īulow, T.: Hypercomplex spectral signal representation for the processing and analysis of images (Ph.D. Master’s Thesis, Institute for Mathematical science, University of Copenhagen (2003)įolland, G.B., Sitaram, A.: The uncertainty principle: a mathematical survey. ![]()
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