Convolution and a specific function

In summary, the conversation discusses the use of convolution with the Dirac Delta function in order to evaluate a given function at a specific point. The question is whether there exists a function g that, when convolved with f, would give the evaluation of f at a given point y1. It is suggested that DiracDelta[x-y1] can be used for this purpose. One participant requests further clarification on the definition of convolution.
  • #1
Littlepig
99
0
Hi there.

We know that Convolve[f,g,x,y] = f[y] if g = diracdelta. My question is, what should be g so that Convolve[f,g,x,y] = f[y1] where y1 is a parameter of the g function. I.e. Is there any function g such that, when convolved with another f, gives the evaluation of f on a given point?
 
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  • #2
Yep, simply DiracDelta[x-y1] does the deal.
 
  • #3
Can you make your statement a bit more clear. how are you defining the convolution?

Littlepig said:
Hi there.

We know that Convolve[f,g,x,y] = f[y] if g = diracdelta. My question is, what should be g so that Convolve[f,g,x,y] = f[y1] where y1 is a parameter of the g function. I.e. Is there any function g such that, when convolved with another f, gives the evaluation of f on a given point?
 

1. What is convolution and how is it used in science?

Convolution is a mathematical operation that combines two functions to produce a third function. In science, it is often used to analyze the relationship between two quantities, such as time and distance, by representing them as functions and then convolving them to determine the resulting function.

2. How does convolution affect the shape of a function?

The shape of a convolved function is determined by the shape of the two original functions being convolved. The resulting function will have features that are a combination of the features of the original functions, such as peaks and valleys.

3. What is the difference between discrete and continuous convolution?

Discrete convolution is used when dealing with functions that are defined at specific points or intervals, such as digital signals. Continuous convolution, on the other hand, is used when dealing with functions that are defined over a continuous range, such as physical measurements.

4. How is convolution related to the concept of filtering?

Convolution is often used in signal processing as a way to filter out unwanted noise or frequencies from a signal. By convolving the signal with a specific filter function, certain frequencies can be amplified or attenuated, resulting in a cleaner signal.

5. Can convolution be applied to non-mathematical functions?

Yes, convolution can be applied to any type of function, not just mathematical ones. In science, it is often used to analyze the relationship between two physical quantities, such as temperature and pressure, by representing them as functions and then convolving them to determine the resulting function.

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