Bessel functions are a family of special functions that arise in many areas of mathematical physics and engineering. In particular, the Bessel functions of the first kind and nth order play a key role in frequency modulation (FM) of radio signals. Sidebands appear in the spectra of the FM transmit signal - above and below the carrier frequency. For each of the nth-order sidebands the amplitude is determined by Jn(x), where x is the index of modulation. Overall, Bessel functions are an important mathematical tool for analyzing and designing systems in communication theory, especially for circularly symmetric systems and for modulation techniques such as FM.
