Rectangular function: Difference between revisions

Revision as of 20:11, 14 October 2022

Revision as of 22:47, 2 November 2022

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\end{array}\right.</math>

Alternative definitions of the function define <math display=inline>\operatorname{rect}\left(\pm\frac{1}{2}\right)</math> to be 0,<ref>{{Cite book |last=Wang |first=Ruye |title=Introduction to Orthogonal Transforms: With Applications in Data Processing and Analysis |pages=135–136 |publisher=Cambridge University Press |year=2012 |url=https://books.google.com/books?id=4KEKGjaiJn0C&pg=PA135 |isbn=9780521516884 }}</ref> 1,<ref>{{Cite book |last=Tang |first=K. T. |title=Mathematical Methods for Engineers and Scientists: Fourier analysis, partial differential equations and variational models |page=85 |publisher=Springer |year=2007 |url=https://books.google.com/books?id=gG-ybR3uIGsC&pg=PA85 |isbn=9783540446958 }}</ref><ref>{{Cite book |last=Kumar |first=A. Anand |title=Signals and Systems |publisher=PHI Learning Pvt. Ltd. |pages=258–260 |url=https://books.google.com/books?id=FGGa6BXhy3kC&pg=PA258 |isbn=9788120343108 |year=2011 }}</ref> or undefined. However, this mid-point property, as defined here, is required (see e.g. Theorem 2, p.&nbsp;241 in <ref>{{Cite book |last=Kaplan |first=Wilfred |title=Operational Methods for Linear Systems |publisher=Addison-Wesley Pub. Co. |year=1962 }}</ref>) to be consistent with Fourier transform theory, otherwise the ''rect'' function is not the Fourier transform of [[Sinc function|''sinc'' function]].

==History==