The Bessel function of the first kind is a special mathematical function that appears in many areas of physics and engineering, including wave propagation, vibrations, and digital signal processing.

In digital signal processing, it is especially important because it is used in the definition of the Kaiser window, one of the most flexible window functions for spectral analysis.

The most commonly used version in DSP is the zero-order modified Bessel function:

This function does not oscillate like sine or cosine functions. Instead, it produces a smooth, symmetric curve that grows in a controlled exponential-like manner.