About: Convolution

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In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. A convolution is a kind of very general moving average, as one can see by taking one of the functions to be an indicator function of an interval.

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rdfs:label	Convolution
rdfs:comment	In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. A convolution is a kind of very general moving average, as one can see by taking one of the functions to be an indicator function of an interval. A mathematical technique of combining two sounds so that the result has both envelope and spectral properties of both sounds. It can be though of as a sort of bi-directional method of resynthesis. In this method of synthesis, two digital signals have individual words combined over a short interval of time. Convolution is often used to generate reverb by this technique: An impulse response of a real reverberant space is recorded. The resulting short sample is then convoluted with an incoming signal. The result sounds like the signal was actually recorded in the reverberant space from which the impulse response was taken.
sameAs	dbr:Convolution
dcterms:subject	Effects Effects Techniques Techniques Math concepts Synthesis methods Math concepts Synthesis methods
abstract	In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. A convolution is a kind of very general moving average, as one can see by taking one of the functions to be an indicator function of an interval. A mathematical technique of combining two sounds so that the result has both envelope and spectral properties of both sounds. It can be though of as a sort of bi-directional method of resynthesis. In this method of synthesis, two digital signals have individual words combined over a short interval of time. Convolution is often used to generate reverb by this technique: An impulse response of a real reverberant space is recorded. The resulting short sample is then convoluted with an incoming signal. The result sounds like the signal was actually recorded in the reverberant space from which the impulse response was taken. The main problem with convolution as a synthesis technique is that, by the nature of the math involved, it cannot produce output exactly in real time. There is always some delay between input and output, and the higher the quality of the computation, the higher the delay. This is the reason that convolution is used mainly for generating reverb, because in that application, a short delay is of little consequence.

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