The speech waveforna of a syllable is a nonlinear, time-varying response system and hence the syllable has also a nonlinear, tim-varying dynamic feature changing with the waveform. The present invention discloses a pattern matching system applicable for syllable recognition which is theoretically and statistically derived based on this nonlinear, time-varying waveform. The invention includes a converting means, using an uniform segmentation on the speech waveform with E small equal elastic frames without filter, half overlapped to stretch or contract themselves to cover the variable length of the whole speech waveform of a known syllable. Since a signal has a linear relation with its previous signals [1,3,4], we approximate the nonlinear, time-varying waveform by a linear regression model in each of E short frames for normalizing and converting the waveform into a sequence of E linear predict coding (LPC) cepstra vectors such that the same j-th elastic frame, j=1,...,E, can produce one by one in order the same LPC cepstra (LPCC) vector by the least squares method for the same syllable. Many speakers pronounce the same known syllable and produce various lengths of nonlinear time-varying waveforms. The E elastic frames can normalize and convert them into the samples of E LPCC vectors such that the same LPCC vectors in the samples are pulled into the same time positions in the sequence of E vectors. The sample means and sample variances of LPCC are stored in a database as an equal sized standard pattern to represent the feature of the known syllable. The pattern matching system further includes a converting means, using an uniform segmentation on the speech waveform of an unknown syllable with E small equal elastic frames without filter, half overlapped to stretch or contract themselves to cover the variable length of the whole speech waveform of the unknown syllable, for normalizing and converting the waveform of the input unknown syllable into an equal sized categorizing pattern of E LPC cepstra vectors representing the unknown syllable. The pattern matching system further includes a Bayesian categorizing means for matching the equal sized stan- dard pattern representing a known syllable and the equal sized categorizing pattern representing an unknown syllable by computing a Bayesian misclassification prob- ability for each of the known syllables. The Bayesian categorization means further includes a comparing and identification means for selecting a known syllable which has the least misclassification probability as an identified syllable for the input unknown syllable. In the pattern matching system of the invention, one advantage is that elastic frames normalize the various length of waveform before extract the feature of an unknown syllable and as soon as the feature is extracted, the simplifed Bayes rule is immediately and readily able to classify the unknown syllable without additional normalizing, adjusting, compressing or warping the feature pattern as in the dynamic time-warping methods. Another advantage of the invention is that E elastic frames can pull the same features to the same time positions in the feature pattern from the different waveforms representing the same syllable. Another advantage of the invention is that elastic frames can adjust too short or too long waveforms pronounced in a fast or slow speech and convert the waveforms into equal sized feature patterns which are immediately able to be classified. This raises recogni- tion applicability for the invention, especially for English words made of short basic phonemes. The pattern matching system in the invention has the following features: (1) The pattern recognition system is statistically and theoretically derived based on the nonlinear time-varying waveforms without any arbitrary, artificial or experimental adjustments for better pattern recognition. (2) Since the waveform of a syllable is normalized before feature extraction, E equal elastic frames can use the same j-th elastic frame, j=1,...,E, to catch one by one in order the same LPC feature vector for the same syllable and the different LPC feature vectors for different syllables. (3) The system can be readily and immediately used without additional training and computing for thresholds and parameters. (4) The waveform normalization before feature extraction by E equal elastic frames saves the computation time in training and recognition. (5) The waveform normalization before feature extraction by E equal elastic frames significantly increases recognition rates. (6) The waveform normalization before feature extraction by E equal elastic frames significantly simplifies the algorithms used in the pattern matching system. (7) The waveform normalization before feature extraction by E equal elastic frames increases the applicability of the speech recognition system, i.e., the E equal elastic frames stretch or contract themselves to cover the whole speech waveform denoting a syllable to produce an equal sized pattern of E LPC cepstra vectors by the least squares method denoting the syllable and hence the pattern recognition system in the invention can recognize the syllables with too short or too long speech waveforms, especially English words made of short basic phonemes. (8) The waveform normalization before feature extraction with E equal elastic frames provides a simple feature easily extracted from speech signal waveform. (9) The Bayesian categorizing means needs less time for classification on an equal sized categorizing pattern of LPC cepstra which have normal distributions and has the least mis-classification probability and hence provides higher recognition rates.