Group time and bandwidth of signals modulated simultaneously in amplitude and frequency

Spectral analysis of a frequency and amplitude imbricated signal is considered, with attention given to time lags due to the overlapping of signal characteristics. A numerical model is developed for the frequency-time depiction of the energy of a signal modulated in frequency and time. Approximations are devised for cases where either the amplitude or frequency variation is dominant. Exact calculation of the spectra of a signal modulated linearly in frequency and in a gaussian manner in amplitude is employed to evaluate the wave band of a signal and the group duration. Further studies to model nonlinear variations in frequency or of multiple components are indicated.