Matching Pursuit (MP) a method of high-resolution signal analysis is described in the context of other methods operating in time-frequency space. The method relies on an adaptive approximation of a signal by means of waveforms chosen from a very large and redundant dictionary of functions. The MP performance is illustrated by simulations and examples of sleep spindles and slow wave activity analysis. An improvement of the original procedure, relying on the introduction of stochastic dictionaries, is proposed. A comparison of the performance of dyadic and stochastic dictionaries is presented. MP with stochastic dictionaries is characterized by an unmatched resolution in time-frequency space; moreover it allows for parametric description of all (periodic and transient) signal features in the framework of the same formalism. Matching pursuit is especially suitable for analysis of non-stationary signals and is a unique tool for the investigation of dynamic changes of brain activity.