In arithmetic, convolution is the mathematical operation of two features (a and b), which creates a 3rd function (a * b) that represents how the form of one characteristic is modified via another feature. it is also defined because the critical of the made of any two features after one characteristic is inverted and shifted. So, calculate the fundamental of all offset values ββto attain the convolution function. $$ (a * b) (t) := ∫_-∞^∞b(r) a(t – r) dr $$
Example 1:
Write first data sequence (A) = 0.5, 0.2, 0.8, 1, 0.3
Then, write second data sequence (B) = 0.1, 0.7, 0.9
By using the convolution formula:
$$ (a * b) (t) := \int_{-\infty}^{\infty} b(r) a(t - r) \, dr $$
Thus, the result data sequence (C) = 0.05, 0.39, 0.95, 1.48, 1.2, 0.27, 0.0
Example 2:
Put the first data sequence (A) = 0.8, 1, 0.4, 0.3, 0.2, 0.1
Now, put the second data sequence (B) = 0.3, 0.5, 0.4, 0.2, 0.1
With the help of the convolution integral formula:
$$ (a * b) (t) := \int_{-\infty}^{\infty} b(r) a(t - r) \, dr $$
Hence, the result data sequence (C) = 0.24, 0.79, 1.36, 1.42, 1.17, 0.95, 0.67, 0.25, 0.1
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