(untitled) (International Journal of Latest Technology in Engineering Management & Applied Science, 2026)
This work presents a comprehensive spectral analysis for bandwidth estimation of phase-modulated (PM) signals using Bessel functions of the first kind. The mathematical framework of phase modulation is developed and expressed through Fourier–Bessel expansion, revealing the role of modulation index in determining sideband amplitudes and spectral distribution. Numerical simulations confirm theoretical predictions and demonstrate the redistribution of carrier power among sidebands with increasing phase deviation. The results provide analytical insight useful for communication system design and bandwidth optimization.