This thesis develops relevant definitions and a theoretical basis for estimating the repetition rate of a random repetitive signal. The repetition rate is estimated by looking for repetition amongst local features of the signals. These features have to satisfy a uniqueness condition, and we have shown that the derivatives of a signal constitute a set of such features. The estimator has been shown to be asymptotically unbiased. The estimation algorithm can not only be tuned to the waveshape information of the signal (by a proper choice of features), but also to the extent of non-stationarity expected in the input signal class. A set of features has been obtained for applying this algorithm to repetitive textured images and voiced speech signals. Vith these features, it has been possible to extract the repetition rate in both the above classes of signals. In the case of voiced speech this rate corresponds to its pitch.