- #1
benndamann33
- 22
- 0
anyone know how to prove that it is commutative...
as if f *g = g*f
as if f *g = g*f
Convolution is a mathematical operation that combines two functions to create a third function. It is commonly used in signal processing and image processing to extract features or filter out noise.
Convolution is performed by taking one of the functions (often referred to as the "input" function) and flipping it horizontally and vertically. This flipped function is then slid over the other function (often referred to as the "kernel" function), multiplying and summing their values at each point, to create the third function (often referred to as the "output" function).
The commutative property of convolution states that the order in which the two functions are convolved does not affect the final result. In other words, if function A is convolved with function B, the result will be the same as if function B was convolved with function A.
The commutative property of convolution can be proven using the mathematical definition of convolution and the properties of integrals. By swapping the order of integration and changing the variables, it can be shown that the result of convolving two functions is the same regardless of the order in which they are convolved.
The commutative property of convolution is important because it allows for greater flexibility in performing mathematical operations. It also allows for simplification of calculations, as the order in which the functions are convolved does not affect the result. This property is commonly used in various fields such as signal processing, image processing, and machine learning.