Convolution
Convolution is the integral transform that expresses the amount of overlap of one function g as it is shifted over another function f.
Convolution is a college-level concept that would be first encountered in an analysis course.
Examples
| Fourier Transform: |
A Fourier transform is a generalization of complex Fourier series that expresses a function in terms of frequency components. Fourier transforms arise quite commonly not only in mathematics, but also in optics, signal processing, and many other areas of science and engineering. |
| Laplace Transform: |
The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly useful in solving linear ordinary differential equations such as those arising in the analysis of electronic circuits. |
Prerequisites
| Integral: |
An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals and derivatives are the fundamental objects of calculus. |
Classroom Articles on Analysis (Up to College Level)
