Ambiguity function: Difference between revisions

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The ambiguity function plays a key role in the field of [[time–frequency signal processing]],<ref>E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” ''Digital Signal Processing'', vol. 19, no. 1, pp. 153-183, January 2009.</ref> as it is related to the [[Wigner–Ville distribution]] by a 2-dimensional [[Fourier transform]]. This relationship is fundamental to the formulation of other [[time–frequency distribution]]s: the [[bilinear time–frequency distribution]]s are obtained by a 2-dimensional filtering in the ambiguity ___domain (that is, the ambiguity function of the signal). This class of distribution may be better adapted to the signals considered.<ref>B. Boashash, editor, “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003; {{ISBN|0-08-044335-4}}</ref>

Moreover, the ambiguity distribution can be seen as the [[short-time Fourier transform]] of a signal using the signal itself as the window function. This remark has been used to define an ambiguity distribution over the time-scale ___domain instead of the time-frequency ___domain.<ref>Shenoy, R.G.; Parks, T.W., "Affine Wigner distributions," IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-92., pp.185-188 vol.5, 23-26 Mar 1992, [httphttps://dx.doi.org/10.1109/ICASSP.1992.226539 doi: 10.1109/ICASSP.1992.226539]</ref>

==Wideband ambiguity function==