Time-Frequency Analysis —G(λ)-stationary Processes

Methods such as wavelets and M-stationary process have been developed to analyze the time-frequency properties of a process where frequency changes with time. In certain circumstances, when the frequencies of a process change systematically either monotonically increasing or monotonically decreasing across time, another approach is to apply an appropriate Box-Cox transformation to the time axis for the given signal in order to obtain a new stationary data set. This new data set can be analyzed by standard methods. Processes which are transformed to a stationary process after Box-Cox transformation on the time scale are called G(λ)-stationary processes, where λ is the corresponding parameter of the Box-Cox transformation. The method is illustrated with analysis of both simulated and real data. Finally, it is shown that such processes can be transformed to stationarity by sampling properly.