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Although the Discrete Cosine Transform (DCT) is wide{v used for feature extraction in pattern recognition, it is shown that it converges slowly for most theoretically smooth functions. A modification of the DCT is described, based on a change of variable, which changes it to a new transform, called the Discrete Chebyshev Transform DCh T, which converges vel)' rapidly for the same smooth functions. Although this rapid convergence is largely destroyed by the noise in real experimental data, the Discrete Chebyshev Transform is still generally better than the DCT when the sampling of the data can be selected at non-equidistant points. The improvement over the DCT gives a theoretical explanation for improved speech recognition obtained using Mel Feature Cepstral Coefficients. These choose the sampling frequencies of a DCT to correspond to the human perception of pitch. It is shown that this sam p ling is similar to the .�ampIing used in the Discrete Chebyshev Transform.

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Closest-vector selection is a process that underlies one technique for sending compressed-signal sets over noisy communication channels. Recently it has had application in radar target identification, speech and image analysis, pattern classification, and neural-net training. Various applications of closest-vector selection are discussed, and the design of an all-optical system that performs closest-vector selection is presented.