  The nonstationary nature of signals and nonlinear systems require the
time-frequency representation. In time-domain signal, frequency information is
derived from the phase of the Gabor's analytic signal which is practically
obtained by the inverse Fourier transform. This study presents time-frequency
analysis by the Fourier transform which maps the time-domain signal into the
frequency-domain. In this study, we derive the time information from the phase
of the frequency-domain signal and obtain the time-frequency representation. In
order to obtain the time information in Fourier domain, we define the concept
of `frequentaneous time' which is frequency derivative of phase. This is very
similar to the group delay, which is also defined as frequency derivative of
phase and it provide physical meaning only when it is positive. The
frequentaneous time is always positive or negative depending upon whether
signal is defined for only positive or negative times, respectively. If a
signal is defined for both positive and negative times, then we divide the
signal into two parts, signal for positive times and signal for negative times.
The proposed frequentaneous time and Fourier transform based time-frequency
distribution contains only those frequencies which are present in the Fourier
spectrum. Simulations and numerical results, on many simulated as well as read
data, demonstrate the efficacy of the proposed method for the time-frequency
analysis of a signal.
