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A functional representation of speech sounds in orthogonal polynomial space is described and preliminary results are presented. Speech spectra are approximated by a linear combination of orthogonal polynomials which are found to be more efficient than a linear combination of trigonometric functions. The original spectra (100 samples in frequency) and the polynomial approximations are represented by points in their respective Hilbert spaces, the distance between successive points being a measure of the dissimilarity of successive spectra. Segment boundaries are indicated where the distance between successive spectra exceeds a threshold. The effectiveness in segmentation of connected utterances using these spectral forms is compared. Also, representing speech in orthogonal polynomial space appears to be applicable to clustering and separating transformations which yield simple decision boundaries for phoneme classification. Although only one polynomial class is investigated, the procedure is valid for other functional representations of speech data.