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Time-frequency analysis techniques are used to produce a plot of a signal's power spectrum as a function of time. The most well-known time-frequency representation is the spectrogram. Although relatively simple to compute, it suffers from having a significant limitation in that it cannot offer good time or frequency resolution simultaneously. To overcome this weakness, many other representations have been developed that provide combined high resolution over time and frequency. The Wigner-Ville distribution, the scalogram, and the discrete Gabor transform are among the most well-known of these methods. Due to specific shortcomings with regard to these distributions for multi-component signals, and for certain mathematical concerns such as shift invariance and time and frequency marginal conditions, several classes of representations have been developed which effectively address specific signal types. Examples of these categories are Cohen's class, the affine class, and the signal adaptive expansions based upon the Matching Pursuit method. The goals of any of these specific methods are to minimize cross-term interference, provide good time and frequency resolution, and provide a good model for the signal of interest.