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enter image description here

what must be the equation to get this type of a curve??

the curve must increase from -infinity to 0 and then decrease again to +infinity.

Thank you

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Such a curve is not algebraic: those are by definition given by polynomials and intersect each line (or other curve) in finitely many other points by Bézout.. That is clearly not the case in your picture.. –  Joachim Aug 18 '12 at 6:45
    
(There used to be a tag "algebraic-curves") –  Joachim Aug 18 '12 at 8:09

2 Answers 2

up vote 5 down vote accepted

You can try multiplying a $\sin$ wave with a Gaussian, e.g: $$\sin(5x)e^{-x^2/2}$$ enter image description here

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Related: Gabor filter, Morlet wavelet. –  Rahul Aug 18 '12 at 6:56

y=sin(x)/x has this property.
sin(x)/x function has a special name: sinc(x)
It is an important function. For example it is the Fourier transform of the rectangular pulse which plays a major role in signals and systems analysis.

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The sine cardinal is an even function, while the OP's function does not at all look even... –  J. M. Aug 18 '12 at 6:50
    
@J.M. I don't think the OP wants the function to be even. I mean if he wanted the function in the figure then how did he plot it? –  Zeta.Investigator Aug 18 '12 at 6:54
    
Still, the graph of the function you propose looks nothing like the OP's picture... –  J. M. Aug 18 '12 at 6:56

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