Convolution in digital signal processing

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Convolution is a formal mathematical operation, just as multiplication, addition, and integration. Addition takes two numbers and produces a third number, while convolution takes two signals and produces a third signal.
 
 
Convolution is used in the mathematics of many fields, such as probability and statistics. In linear systems, convolution is used to describe the relationship between three signals of interest: the input signal, the impulse response, and the output signal.
 
 

An input signal, x[n], enters a linear system with an impulse response, h[n], resulting in an output signal, y[n]. In equation form: x[n] * h[n] = y[n].
 
 
Expressed in words, the input signal convolved with the impulse response is equal to the output signal.
 
 
Just as addition is represented by the plus, +, and multiplication by the cross, ×, convolution is represented by the star, *.
 
 
It is unfortunate that most programming languages also use the star to indicate multiplication. A star in a computer program means multiplication, while a star in an equation means convolution.

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