Speaker verification involves the determination of whether or not a test utterance belongs to a specific reference speaker. The utterance is either accepted as belonging to the reference speaker or rejected as belonging to an imposter. Speaker verification has great potential for security applications, such as physical access control, computer data access control, and automatic telephone transaction control. The main components of a general speaker verification system are shown in Fig. 1. A speaker verification task consists of two phases. In the training phase, reference templates are created for particular speakers using the signal processor shown in Fig. la. During the uerification phase (Fig. lb), the identity claimed by a speaker is verified using a test utterance from that speaker. The inputs to the system consist of a test utterance (sampled at 10 kHz in our experiments) and the claimed identity of the reference speaker. The signal processor can be further subdivided into three steps: normalization, parameterization, and feature extraction. These steps involve preprocessing and information reduction (or elimination of redundancies) in the input data sequence to obtain speaker templates during the training and verification phases. The normalization step consists of noise reduction, signal amplitude level control, and time warping to reduce the effect of different speaking rates. This is followed by the parameterization step to reduce the amount of data with minimal information loss about the speaker characteristics. An optional feature extraction step can be used to further reduce the data. Next the test template is compared to the reference template. The accept/reject decision is usually based on the computation of a distance function which quantifies the degree of dissimilarity between the test template and the reference template [l] . If the distance exceeds a threshold, the system rejects the match. Comparing the test and the training templates in the verification phase is much simpler if the underlying texts of the utterances are the same. Normally, this text-dependent mode is possible only for cooperative speakers. In forensic work, for example, speakers are often uncooperative, and the test and the training texts are often not the same. This mode is called textindependent speaker verification and the required information stored in the templates is different in this case. In general, the templates contain long-term statistical data. Error rates for text-independent recognition are considerably higher than the rates for a comparable text-dependent case. In this paper, we investigate text-independent speaker verification. A speaker verification system produces two types of errors. Type I error is caused when a true speaker is rejected as being an imposter. Type II error results when an imposter is accepted by the system as the correct speaker. Naturally, the objective in a verification task is to minimize both errors. Previous work [l, 21 on automatic text-independent speaker verification suggests that the important features for speaker discrimination are the spectral envelope parameters. Generally, in speaker verification systems, the reference speaker templates are obtained by averaging short-time spectral parameters over the complete speech utterance. In other words, an average vocal-tract shape is assumed for the duration of the utterance. However, this does not hold in practice since it is well known that different sounds are produced by vocal-tract shapes that vary widely