The Convolution is a mathematical operation that applies on any two values, say ‘A’ and ‘F.’ This results in a third value as an output say ‘B’. In convolution, one does point to point multiplication of input functions and gets our output function.
A convolution is an integral that exhibits the amount of overlap of one function as it is shifted over another function. Hence, it “blends” in one function with another function.
For instance, in synthesis imaging, the measured dirty map is a convolution by itself of the “true” CLEAN map with the dirty beam (referred to as the Fourier transform of the sampling distribution).
The convolution is sometimes also known by its German side name, faltung (called the “folding”). A Convolution is mostly implemented in the Wolfram Language as Convolve [f, g, x, y] and in Discrete Convolve as [f, g, n, m].
Abstractly, a convolution is mathematically defined as a product of functions f and g that also are objects in the algebra of Schwartz functions in Rπ.
Convolution of two functions f and g over a finite range [0, t] is given as:[f * g] (t) = 0tf (T) g (t – T) dT, where the symbol [f * g] (t) denotes convolution of f and g.