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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.
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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.
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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].
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Expressed in words, the input signal convolved with the impulse response is equal to the output signal.
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Just as addition is represented by the plus, +, and multiplication by the cross, ×, convolution is represented by the star, *.
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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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