How to Calculate Convolution
- 1
Determine H, F, and G.
Determine the two transformed function (F, G). Sometimes, these will be given values; other times, you may have to factor the product function (H). - 2
Inverse transforms of F and G.
Perform an inverse Laplace transform on the functions F and G. Inverse transforms of common functions are available in engineering reference books or textbooks. Some special cases can be calculated directly, but you will most often either have the inverse transform memorized or you must look it up. - 3
Defining the convolution problem.
Use the inverse transforms to build the integral to calculate the convolution and simplify. In this example, the product-to-sum identity converts a multiplication problem involving trigonometric functions into an addition problem. - 4
Solve the integrals.
Solve the resulting integral or integrals.
