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This paper addresses the problem of representing the speech signal using a set of features that are approximately statistically independent. This statistical independence simplifies building probabilistic models based on these features that can be used in applications like speech recognition. Since there is no evidence that the speech signal is a linear combination of separate factors or sources, we use a more general nonlinear transformation of the speech signal to achieve our approximately statistically independent feature set. We choose the transformation to be symplectic to maximize the likelihood of the generated feature set. In this paper, we describe applying this nonlinear transformation to the speech time-domain data directly and to the Mel-frequency cepstrum coefficients (MFCC). We discuss also experiments in which the generated feature set is transformed into a more compact set using a maximum mutual information linear transformation. This linear transformation is used to generate the acoustic features that represent the distinctions among the phonemes. The features resulted from this transformation are used in phoneme recognition experiments. The best results achieved show about 2% improvement in recognition accuracy compared to results based on MFCC features.