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Anamorphic stretch transform
An anamorphic stretch transform (AST) also referred to as warped stretch transform is a physics-inspired signal transform that emerged from photonic time stretch and dispersive Fourier transform. The transform can be applied to analog temporal signals such as communication signals, or to digital spatial data such as images.〔http://newsroom.ucla.edu/portal/ucla/ucla-research-team-invents-new-249693.aspx〕〔http://www.photonics.com/Article.aspx?AID=55602〕 The transform reshapes the data in such a way that its output has properties conducive for data compression and analytics. The reshaping consists of warped stretching in Fourier domain. The name “Anamorphic” is used because of the metaphoric analogy between the warped stretch operation and warping of images in anamorphosis〔J. L. Hunt, B. G. Nickel, and C. Gigault, "Anamorphic images", American Journal of Physics 68, 232–237 (2000).〕 and surrealist artworks.〔Editors of Phaidon Press (2001). "The 20th-Century art book." (Reprinted. ed.). London: Phaidon Press. ISBN 0714835420.〕〔http://www.scienceagogo.com/news/20131120231425.shtml〕
== Operation principle ==
An anamorphic stretch transform (AST)〔M. H. Asghari and B. Jalali, "Anamorphic transformation and its application to time-bandwidth compression", Applied Optics, Vol. 52, pp. 6735-6743 (2013). ()〕〔M. H. Asghari and B. Jalali, "Demonstration of analog time-bandwidth compression using anamorphic stretch transform", Frontiers in Optics (FIO 2013), Paper: FW6A.2, Orlando, USA. ()〕 is a mathematical transformation in which analog or digital data is stretched and warped in a specific fashion such that it results in nonuniform Fourier domain sampling. The detailed of the reshaping depends on the sparsity and redundancy of the input signal and can be obtained by a mathematical function called stretched modulation distribution or modulation intensity distribution (not to be confused with a different function of the same name used in mechanical diagnostics). A stretched modulation distribution is a 3D representation of a type of bilinear time–frequency distribution〔L. Cohen, Time-Frequency Analysis, Prentice-Hall, New York, 1995. ISBN 978-0135945322〕〔B. Boashash, ed., “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003.〕〔S. Qian and D. Chen, Joint Time-Frequency Analysis: Methods and Applications, Chap. 5, Prentice Hall, N.J., 1996.〕 that describes the dependence of intensity or power on the frequency and time duration of the modulation. It provides insight on how information bandwidth and signal duration are modified upon nonlinear dispersion in the time domain, or upon nonlinear diffraction in the spatial domain.〔J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill Book Co (1968).〕
The mathematical transformation emulates propagation of the signal through a physical medium with specific dispersion and diffraction properties,〔T. Jannson, "Real-time Fourier transformation in dispersive optical fibers", Opt. Lett. 8, 232–234 (1983).〕〔D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves", Nature 450, 1054–1057 (2007).〕〔B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias and J. M. Dudley, "Real-time full bandwidth measurement of spectral noise in supercontinuum generation", Scientific Reports 2, Article number: 882 (2012).〕 but with an engineered nonlinear kernel.
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