konvolúciójának

Konvolúciójának is a Hungarian term that translates to "its convolution" in English. In mathematics, convolution is a mathematical operation that takes two functions and produces a third function. This third function represents how the shape of one function is modified by the other. It is often described as a "weighted average" or "blending" of one function by another.

The concept of convolution is fundamental in various fields. In signal processing, it's used to describe the output of a linear time-invariant system when a specific input signal is applied. For example, an audio filter's effect on a sound wave can be represented by a convolution. In image processing, convolution is used for operations like blurring, sharpening, and edge detection, where a kernel (a small matrix) is convolved with the image.

The mathematical definition of convolution for two functions, f and g, is typically given by an integral. For continuous functions, the convolution of f and g, denoted by (f * g)(t), is defined as the integral of f(τ)g(t - τ) with respect to τ, from negative infinity to positive infinity. For discrete functions or sequences, a summation replaces the integral. The term "konvolúciójának" specifically refers to the convolution of something with a particular function or operation, implying a possessive or genitive case in Hungarian.