What is convolution?

Convolution is an important operation in analytical mathematics.

The convolution formula is only used to calculate the density function, not the distribution function. In functional analysis, Convolution, convolution or convolution (English: convolution) is a mathematical operator that generates a third function from two functions F and G, representing the accumulation of overlapping parts of functions F and G after flipping and translation. If the function involved in convolution is regarded as interval indicator function, convolution can also be regarded as a generalization of "moving average".

Convolution is a mathematical method of integral transformation, which is widely used in many aspects. Using convolution to solve the problem of well test interpretation has achieved good results for a long time, but deconvolution has recently solved the stability problem of its calculation method, which has quickly attracted widespread attention in the field of well test.

Formula of discrete convolution: Here, the domain of I is from negative infinity to positive infinity. Of course, specific problems need specific analysis, such as grades (100), then the definition of I is (0- 100). Formula of continuous convolution: The lower limit of definite integral here is negative infinity and the upper limit is positive infinity. In the same way, the specific situation is analyzed. If it is still a scoring situation, the lower limit is 0 and the upper limit is 100.