In this thesis, phase and frequency modulation, used mainly in communication theory, is being the major issue. In particular, the thesis emphases phase modulation. Phase and frequency modulation are two different ways to transform signals, so they can more easily be transmitted and received. The equations for these transformations are being considered. Some methods for reconstruction of the signals are implemented and tested. Also, the problem with noisy signals is being dealt with. Further on, an extensive analysis of the Fourier coefficients of such transformed signals and their connection to Bessel functions is performed. Finally the connection between Bessel functions an the energies of these modulated signals is studied using analytic methods and computer experiments.