       Re: FourierTransform of Sign^2 ?

• To: mathgroup at smc.vnet.net
• Subject: [mg80041] Re: FourierTransform of Sign^2 ?
• From: Hendrik van Hees <hees at comp.tamu.edu>
• Date: Sat, 11 Aug 2007 02:09:05 -0400 (EDT)
• Organization: Texas A&M University
• References: <f9gv9e\$b82\$1@smc.vnet.net>

```Jung-Tsung Shen wrote:

> I tried to evaluate the following Fourier Transform:
>
> FourierTransform[Sign[y] Sign[y], y, q]
>
> where Sign is the sign function. Instead of Sqrt[2 Pi]*DiracDelta[q],
> Mathematica (v. 5.0, Mac) gives
>
> -Sqrt[2 Pi]*DiracDelta[q]
>
> with a minus sign. Is this a bug or I am doing something wrong here?

If it's of any interest. I've a pretty old version of Mathematica (4.0
Student Version), and I get the right result only after manual intervention
simplifying UnitStep[y]^2 to UnitStep[y]:

In:= FourierTransform[Sign[y]^2, y, q] /. {UnitStep[y]^2 -> UnitStep[y]}

Out= Sqrt[2 Pi] DiracDelta[q]

--
Hendrik van Hees                        Texas A&M University
Phone:  +1 979/845-1411                 Cyclotron Institute, MS-3366
Fax:    +1 979/845-1899                 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq       mailto:hees at comp.tamu.edu

```

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