Instantaneous frequencies of signals obtained by the analytic signal method

Abstract

In this paper, the instantaneous frequency is defined as the one obtained by converting a real time signal to a complex analytic signal and by differentiating the time-dependent phase with respect to time. Theoretical expressions of instantaneous frequencies for signals given as combinations of sinusoidal components are presented. Those are compared to the results obtained by numerical methods using the discrete Fourier transform in order to confirm the validity of the expressions and to check accuracies of the numerical methods. A reason for the existence of negative instantaneous frequencies is given by a vector representation of signal components. The instantaneous frequencies of frequency- and amplitude-modulated signals are also discussed. For a periodic sinusoidal burst signal, it was found that the instantaneous frequency stays zero during the period when the signal is zero and takes a value equal to twice that of the sinusoid at the onset of the signal.