Convolution is a formal mathematical operation that takes two signals to produce a third signal.

 

Convolution is one of the most frequently used operations in DSP.  It is the basic operation in digital filtering.  Given two finite and causal sequences, and , of lengths and , respectively, their convolution is defined as

 

 

where the symbol is used to denote convolution.

 

Deconvolution is the opposite of convolution. Given a convolved signal and the filter used for convolution, this operation will produce the original signal.

 

 

Figure 1.  A convolution operation