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Nonstationarity relates to the variation over time of the statistics of a signal. Therefore, signals from practical applications that are realizations of nonstationary processes are difficult to represent and to process. In this article, we provide a comprehensive discussion of the asynchronous representation and processing of nonstationary signals using a time-frequency framework. Power consumption and type of processing imposed by the size of the devices in many applications motivate the use of asynchronous, rather than conventional synchronous, approaches. This leads to the consideration of nonuniform, signal-dependent level-crossing (LC) and asynchronous sigma delta modulator (ASDM)-based sampling. Reconstruction from a nonuniform sampled signal is made possible by connecting the sinc and the prolate spheroidal wave (PSW) functions?a more appropriate basis. Two decomposition procedures are considered. One is based on the ASDM that generalizes the Haar wavelet representation and is used for representing analog nonstationary signals. The second decomposer is for representing discrete nonstationary signals. It is based on a linear-chirp-based transform that provides local time-frequency parametric representations based on linear chirps as intrinsic mode functions (IMFs). Important applications of these procedures are the compression and processing of biomedical signals, as it will be illustrated in this article.