 Window function

A window function is a function that vanishes outside a chosen finite interval; multiplying an input by it selects and weights that part of the history before a Fourier transform. The rectangular window $w_T$ is the indicator function of $[0,T]$. Applied to the weighted causal extension by zero of an input, it produces the finite-history integral ${\int }_0^T{e}^{-st}f(t)dt$ used to approximate a Laplace transform.

In SQL and other data processing frameworks, a **window function** is a type of function that performs calculations across a set of table rows that are related to the current row. Unlike regular aggregate functions, which return a single value after grouping rows, window functions allow you to perform calculations across multiple rows while still retaining the individual row details in the output. Window functions are often used for tasks such as calculating moving averages, running totals, and ranking.