convolves

The term "convolves" typically refers to the mathematical operation of convolution. Convolution is a mathematical operation on two functions that produces a third function. This third function represents how the shape of one of the input functions is modified by the other. It is a way of combining two signals to produce a third signal, where the output is a weighted average of the input signal, with the weights determined by the other signal.

In essence, convolution can be thought of as a sliding window operation. One function, often called the kernel or filter, is slid across another function. At each position, the product of the overlapping portions of the two functions is integrated. This integral value becomes a point in the resulting convolved function. The process is used in various fields, including signal processing, image processing, probability theory, and machine learning.

In signal processing, convolution is used for filtering. For example, applying a low-pass filter to a signal involves convolving the signal with the filter's impulse response. In image processing, convolution is fundamental to operations like blurring, sharpening, and edge detection, where a kernel is convolved with the image pixels. In probability, the convolution of two probability density functions gives the probability density function of the sum of two independent random variables. In deep learning, convolutional neural networks utilize convolution operations extensively to extract features from data.