Machinery operating in non-stationary mode generates a signature which at each instant of time has a distinct frequency. A time-frequency domain representation is needed to characterize such signature. Pseudo Wigner-Ville distribution is ideally suited for portraying non-stationary signal in the time- frequency domain and carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner-Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dynamic features jointly in time and frequency. Pseudo Wigner-Ville distribution, Analytic signal, Hilbert transform, Gaussian window, Time- frequency domain.