You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information. |
Table of Contents Bivariate Data Time Series Convolution | |
See also: mathematical details |
Convolution is a phenomenon (or a mathematical procedure, depending on one's standpoint) which is quite common and which is of fundamental importance to signal processing. Before going into mathematical detail, let us consider an example showing the principles of convolution:
A pinhole camera with a (near) zero-diameter pinhole produces a sharp (inverted) image f(x). Each point outside the camera is reproduced perfectly on the film.
If the pinhole has a diameter larger than zero, the image becomes blurred because the image of each point outside the camera is now a spot inside it. This spot contains a distribution of intensities h(x) which are superimposed on points nearby. The distribution function h(x) depends on the shape and the width of the whole.
The inverse process of the convolution is called deconvolution, which is used to extract the sharp signal from a blurred one.
Note, that the concept of convolution is not restricted to images but may also be used in many other situations, e.g. filtering (smoothing) of time series, or correlating two signals, or when considering Fourier transforms and their relation to the time domain signals.
Last Update: 2006-Jän-17