Konvolutsiooniline
Konvolutsiooniline is a term derived from the Latin word "convolutio," meaning "twisting" or "folding." In mathematics, particularly in the field of signal processing and functional analysis, the term "konvolutsiooniline" refers to the convolution operation. Convolution is a mathematical operation on two functions that produces a third function expressing how the shape of one is modified by the other. It is defined as the integral of the product of the two functions after one is reversed and shifted. In the context of discrete signals, convolution is often computed using the discrete convolution formula.
The convolution operation is fundamental in various areas of science and engineering. In signal processing, it
The convolution of two functions f and g is denoted by f * g and is defined as:
(f * g)(t) = ∫ from -∞ to ∞ f(τ) g(t - τ) dτ
In the discrete case, the convolution of two sequences x and y is given by:
(x * y)[n] = ∑ from k=-∞ to ∞ x[k] y[n - k]
The convolution operation has several important properties, including commutativity, associativity, and distributivity. These properties make convolution