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The time-frequency plane Wiener (TFPW) filter is a new method, based on a posteriori Wiener filtering principles, to enhance the performance of ensemble averaging. This paper develops the mathematical aspects of the TFPW filter, and assesses its performance with elementary signals, such as sine waves and chirps, and authentic high-resolution electrocardiogram (HRECG) ensembles. The principal feature of the TFPW filter is its use of the time-frequency plane to accommodate signal nonstationarity. Using a posteriori computed statistics of the ensemble, the filter matches itself to the time-frequency structure of the signal to be estimated. The method is sufficiently general to be applicable to any class of repetitive signal with a deterministic time-frequency structure and additive noise in the ensemble. It is concluded that significant improvements in both estimated signal fidelity and noise reduction are possible with the TFPW filter, compared to conventional ensemble averaging.