||The study of signals whose frequency contents change in time is prevalent in many academic fields. The objective of this thesis is to demonstrate that the joint time-frequency analysis (JTFA) is suitable for the analysis of non-stationary economic time series and business cycles. The joint time-frequency analysis is a signal processing technique in which signals are analyzed in the time domain and the frequency domain simultaneously. One basic problem in business-cycle studies is how to deal with non-stationary time series. The market economy is an evolutionary system. Economic time series therefore contain stochastic components that are necessarily time dependent. Traditional methods of business cycle analysis, such as the correlation analysis and the spectral analysis, cannot capture such historical information because they do not take the time-varying characteristics of the business cycles into consideration. This thesis examines the use of linear and quadratic time-frequency representations to the analysis of non-stationary time series. In particular, the short-time Fourier transform (STFT), the wavelet transform (WT) and the Wigner-Ville distribution (WVD) are presented with emphasis on the wavelet transform and the Wigner-Ville distribution. We first explore the use of joint time-frequency analysis methods through several important test signals, and then we apply these techniques to the analysis of economic time series. The joint time-frequency analysis allows us to characterize and understand not only the historical shocks that trigger the business cycle, but also provide important information regarding the evolution of the business cycle across time. Our analyses show that joint time-frequency analysis is useful for the study of economic time series and should be studied further.