Konvolutsioone

Konvolutsioone, sometimes translated as 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 a fundamental tool in signal processing, image processing, and various areas of mathematics and physics. Imagine one function as a "kernel" or "filter" that slides across another function, the "input signal." At each position, the kernel and the input signal are multiplied element-wise, and the results are summed to produce a single output value. This process is repeated as the kernel moves, generating the output function.

The result of a convolution can be interpreted in several ways. In image processing, for instance, a convolution kernel can be used to blur an image, sharpen it, or detect edges. The kernel defines the local neighborhood of pixels that are averaged or otherwise combined to produce the new value for a pixel in the output image. In signal processing, convolution is used to describe the output of a linear time-invariant (LTI) system when a specific input signal is applied. The impulse response of the system acts as the kernel, and its convolution with the input signal yields the system's output. The mathematical definition involves an integral (for continuous functions) or a summation (for discrete functions) over the product of one function and a time-reversed and shifted version of the other.