# Talk:Rectangular function

WikiProject Mathematics

A perfect example of a rectangular function that I think should be added is:

$R(x) = \lim_{n\to\infty} (\tan\circ\cos)^n(x)$

We already have a much simpler perfect example. Less is more. --Bob K 00:39, 6 June 2006 (UTC)
Nope. — Omegatron 00:42, 8 June 2006 (UTC)

Am I going mad, or is the definition of this simple function just completely wrong? Shouldn't it be

R(x) = 0, if x < -1/2
R(x) = 1, if -1/2 <= x <= 1/2
R(x) = 0, if x > 1/2

????—Preceding unsigned comment added by 213.162.107.11 (talkcontribs)

Is it the values at x = ± ½ that you are concerned about? --Bob K 04:20, 11 July 2006 (UTC)
I am used to seeing this definition in the literature:
$\mathrm{rect}(t) = \begin{cases} 1 & \mbox{if } |t| < \frac{1}{2} \\ 0 & \mbox{if } |t| \geq \frac{1}{2} \end{cases}$
Though I have also seen the current definition ($\mathrm{rect}(\pm 1/2)=1/2$). I just added in a short blurb about the various definitions. --Rabbanis 18:54, 5 August 2006 (UTC)

I added the "As long as the function is motivated by the time-domain experience of it..." clause. I thought it contains insight but I could be mistaken. 77.30.95.216 (talk) 12:35, 7 November 2008 (UTC)

I would like also to comment that it might be better to follow the same convention used in the Fourier Transform article, which uses real frequency for the independent variable in the frequency domain, rather than the other two conventions using angular frequency. But still, I am not a specialist, I just pursue what may be more coherent with the rest of articles, and what may be more intuitive. 77.30.95.216 (talk) 12:51, 7 November 2008 (UTC)

This is not angular frequency:
$\int_{-\infty}^\infty \mathrm{rect}(t)\cdot e^{-i 2\pi f t} \, dt =\frac{\sin(\pi f)}{\pi f} = \mathrm{sinc}(f),\,$
--Bob K (talk) 13:14, 7 November 2008 (UTC)
(blush) Right. Please revise what I have written. It may be inappropriate for the context or simply not needed. I am no specialist. Actually, this is the first time I edit an article, ever :^S. 77.30.95.216 (talk) 15:53, 7 November 2008 (UTC)

My lecturers all call this thing a top-hat function. Is this a normal word for it? I spent about fifteen minutes trying to find this page. Possibly useful redirect? —Preceding unsigned comment added by 82.6.96.22 (talk) 18:53, 7 November 2010 (UTC)