Difference between revisions of "Convolution"

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{{WikiEntry|key=Convolution|qCode=210857}} is a binary mathematical operator.
{{WikiEntry|key=Convolution|qCode=210857}}
 
Convolution is a mathematical operation that expresses the product of two functions. It refers to both the result function and to the process of computing it. After one function is reversed and shifted it could be seen as the integral of the product of the two functions. The following equations is copied from the video: "[[Video/The Convolution of Two Functions Definition & Properties | The Convolution of Two Functions Definition & Properties]]" <ref>{{:Video/The Convolution of Two Functions Definition & Properties}}</ref>
 
The equation of convolution of <math>f</math> of <math>t</math> and <math>g</math> of <math>t</math>:
<math> f(t) * g(t) = \int_{0}^{t} f(\tau) f(t - \tau) d \tau </math>




=[[Convolution]]=
Convolution is a mathematical operation that expresses the product of two functions. It refers to both the result function and to the process of computing it. After one function is reversed and shifted it could be seen as the integral of the product of the two functions.


<math> f(t) * g(t) = \int_{0}^{t} f(\tau) f(t - \tau) d \tau </math>
In this equation, the star between <math>f(t)</math> and <math>g(t)</math> is not multiplication. The star operator:(<math>*</math>), takes two different functions and combines them into one function. The <math>t</math> in the equation is just a variable, and the tau <math>\tau </math> were just the dummy variable of integration.


<ref>{{:Video/The Convolution of Two Functions Definition & Properties}}</ref>
<noinclude>
<ref>{{:Video/Convolutions are not Convoluted}}</ref>
{{PagePostfix
<ref>{{:Video/Introducing Convolutions: Intuition + Convolution Theorem}}</ref>
|category_csd=
}}
</noinclude>

Latest revision as of 13:33, 31 July 2022

Convolution(Q210857)

Convolution is a mathematical operation that expresses the product of two functions. It refers to both the result function and to the process of computing it. After one function is reversed and shifted it could be seen as the integral of the product of the two functions. The following equations is copied from the video: " The Convolution of Two Functions Definition & Properties" [1]

The equation of convolution of of and of :


In this equation, the star between and is not multiplication. The star operator:(), takes two different functions and combines them into one function. The in the equation is just a variable, and the tau were just the dummy variable of integration.


References

  1. ↑ Bazett, Trefor (Apr 12, 2020). The Convolution of Two Functions Definition & Properties. local page: Dr. Trefor Bazett. 

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