Feature vectors encoded by using extrema are known to be immune to different types of distortions of the original time series . This property enables them to be effective in a wide range of pattern matching applications for time series data  . The process of extracting extrema is usually preceded by a filtering step to reduce noise and to bring out prominent features in a time series. The core contribution of this paper is a methodology based on eigenanalysis to optimize the filter that would lead to robust extrema being extracted from the filtered signal. In this context, robustness is understood as the ability of the extrema from a signal to remain intact in spite of distortions to the signal. The paper then demonstrates that the optimally robust' extrema outperform extrema obtained from using traditional filters in a time series pattern matching (subsequence matching) task on real and simulated datasets in the presence of bias, scale factor, and outlier distortions in the query signal.