Approximations to the delta function on a computer

AI Thread Summary
Approximating the delta function for computational use involves understanding its nature as a distribution rather than a conventional function. One effective method is to use a Gaussian function, which can approximate the delta function as its width approaches zero while its height increases accordingly. Additionally, the delta function can be represented in the context of Fourier transforms, particularly using a discrete Fourier transform. Most programming languages facilitate operations involving the delta function, allowing for straightforward convolution by simply evaluating the function at zero. These methods provide practical approaches for implementing delta function approximations in computational applications.
onsagerian
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Hi,
I am looking for approximations to the delta functoin which I can use on a computer. Although I will never get an exact delta function, I can make an approximation that it can be improved as much as I like.

Would you help me to find the approximation of the delta function so that I can put it on the computer?

Thanks,
Best regards
 
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This doesn't make much sense without any context. A delta function is a distribution. If you are interested in integrating over it then that is simply evaluating the function at the delta function. You can represent them in a Fourier transform as a single point if you use a discrete Fourier transform. Another way to approximate it would be a Guassian function as you take the limit of its width to zero and increase its height accordingly.
 
Convolving with the delta function is built-in to most programming languages -- it's simply plugging 0 into a function.
 

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