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MathGroup Archive 2005

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Re: Re: a question about the UnitStep function

Pratik Desai wrote:

>Zhou Jiang wrote:
>>Dear Mathgroup, 
>>I want to let Mathematica compute the convolution of two sqare waves. I did as follows
>>integrand=f[z] f[x-z];
>>Assuming[Element[x, Reals], Integrate[integrand, {z, -Infinity, Infinity}]]
>>Mathematica gave me the result as follows,
>>((-1 + x) UnitStep[-1 + x] - x UnitStep[x] + (2 + x) UnitStep[2 + x])/4
>>I plot the result to check 
>>Plot[%,{x,-10,10}, PlotRange->All];
>>It is clear wrong since the convolution of two square waves should be convergent. Can anyone give me some help with the subtlties about the UnitStep function? Any thoughts are appriciable. 
>Try this,
>integrand1=f[x] f[x-1]
>Hope this is what your are looking for
Hello all,

After seeing other posts, I realize my post was obviously wrong. I 
sincerely apologize for that.  Although my approach using fourier 
transform should work for example if I change my approach as shown 
below, I  get a triangular wave but not what everybody else is getting

Best Regards


Pratik Desai
Graduate Student
Department of Mechanical Engineering
Phone: 410 455 8134

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