m (New page: =Generic Definition= convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amount of overlap between f and...) |
m |
||
| Line 1: | Line 1: | ||
| + | __NOTOC__ | ||
| + | |||
=Generic Definition= | =Generic Definition= | ||
convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amount of overlap between f and a reversed and translated version of g | convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amount of overlap between f and a reversed and translated version of g | ||
| Line 8: | Line 10: | ||
The convolution of two functions results in a new function that is a product of the overlap of the two functions when one is flipped across the x-axis and then shifted from <math>{-\infty}</math> to <math>\infty</math>. It is easily demonstrated visually and can be used to find the output of an LTI system. The output is simply the convolution of the input and the system's impulse response. | The convolution of two functions results in a new function that is a product of the overlap of the two functions when one is flipped across the x-axis and then shifted from <math>{-\infty}</math> to <math>\infty</math>. It is easily demonstrated visually and can be used to find the output of an LTI system. The output is simply the convolution of the input and the system's impulse response. | ||
| − | + | =Active Learning?= | |
| + | Is this really convolution? | ||
| + | {{:Active Learning}} | ||
Latest revision as of 15:22, 20 March 2008
Generic Definition
convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amount of overlap between f and a reversed and translated version of g
Mathematical Definition
$ f \ast g = \int_{-\infty}^{\infty}f(\tau)g(t-\tau)dt $
Descriptive Definition
The convolution of two functions results in a new function that is a product of the overlap of the two functions when one is flipped across the x-axis and then shifted from $ {-\infty} $ to $ \infty $. It is easily demonstrated visually and can be used to find the output of an LTI system. The output is simply the convolution of the input and the system's impulse response.
Active Learning?
Is this really convolution? Active Learning
