See Convolution theorem for a derivation of that property of convolution. The Fourier transform translates between convolution and multiplication of functions. Computing the inverse of the convolution operation is known as deconvolution. Note that for 1-dimensional cubic convolution interpolation 4 sample points are required. Versions of the convolution theorem are true for various Fourier-related transforms. FIR algorithms allows for a zero input-output latency that is useful for real-time convolution computations. That situation arises in the context of the circular convolution theorem. The Volterra series is an extension of the linear convolution integral. The notation () for "cyclic convolution" denotes convolution over the cyclic group of integers modulo. The set of invertible distributions forms an abelian group under the convolution. High levels of precision are necessary for algorithms that involve repeated processing, such as convolution. Neural networks are based on computational models of learning using factor analysis or convolution. This imaging process is usually formulated by a convolution equation. A "discrete convolution" can be defined for functions on the set of integers. See LTI system theory for a derivation of convolution as the result of LTI constraints.