Approximations to the delta function on a computer

In summary, the conversation is about finding approximations for the delta function that can be used on a computer. The speaker mentions that although an exact delta function is not possible, an approximation can be improved. They ask for help in finding an approximation for the delta function to use on the computer. Some suggestions for approximating the delta function include using a discrete Fourier transform or convolving with a Gaussian function.
  • #1
onsagerian
3
0
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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  • #2


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.
 
  • #3
Convolving with the delta function is built-in to most programming languages -- it's simply plugging 0 into a function.
 

1. What is the delta function?

The delta function, denoted as δ(x), is a mathematical function that is defined as zero at all values of x except at x=0, where it is infinite. It is often used in physics and engineering to represent a point source or an idealized impulse.

2. Why do we need approximations to the delta function on a computer?

Computers cannot handle infinite values, so the delta function cannot be directly represented on a computer. Therefore, we need to use approximations to the delta function in order to perform calculations and simulations on a computer.

3. What are some common approximations to the delta function on a computer?

Some common approximations to the delta function on a computer include the box function, the Gaussian function, and the sinc function. These approximations have different properties and are used in different applications.

4. How accurate are these approximations to the delta function?

The accuracy of these approximations depends on the specific application and the desired level of precision. In general, the accuracy of these approximations improves as the width of the function decreases, but this also increases the computational cost.

5. Can these approximations be used in all types of computer simulations?

No, these approximations may not be suitable for all types of computer simulations. They are most commonly used in numerical methods and simulations that involve continuous functions. In some cases, other techniques such as discrete convolution may be used to approximate the delta function on a computer.

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