Convolution

The *convolution* of two signals
and
in
may be
denoted ``
'' and defined by

Note that this is

Cyclic convolution can be expressed in terms of previously defined operators as

where and . This expression suggests

- Commutativity of Convolution
- Convolution as a Filtering Operation
- Convolution Example 1: Smoothing a Rectangular Pulse
- Convolution Example 2: ADSR Envelope
- Convolution Example 3: Matched Filtering
- Graphical Convolution
- Polynomial Multiplication
- Multiplication of Decimal Numbers

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University