This paper presents a new technique for automatic speaker verification using telephone speech. The system operates by extracting cepstrum coefficients from a fixed, sentence-long utterance through LPC analysis, removing frequency response distortions, and expanding the time functions using orthogonal polynomial representations. The time functions are then registered with stored reference functions to calculate an overall distance, which is used to decide on the identity claim. The system evaluates several experimental utterances, including male and female speakers recorded over conventional telephone connections, and shows an error rate of one percent or less even under different transmission conditions. The paper details the system's operation, including cepstrum extraction, polynomial coefficient representation, time registration, and distance calculation. It also discusses the selection of reference functions and decision thresholds, and evaluates the system's performance under various transmission systems and artificial transmission variations. The results demonstrate the system's effectiveness in speaker verification, even when there are significant differences in transmission characteristics.This paper presents a new technique for automatic speaker verification using telephone speech. The system operates by extracting cepstrum coefficients from a fixed, sentence-long utterance through LPC analysis, removing frequency response distortions, and expanding the time functions using orthogonal polynomial representations. The time functions are then registered with stored reference functions to calculate an overall distance, which is used to decide on the identity claim. The system evaluates several experimental utterances, including male and female speakers recorded over conventional telephone connections, and shows an error rate of one percent or less even under different transmission conditions. The paper details the system's operation, including cepstrum extraction, polynomial coefficient representation, time registration, and distance calculation. It also discusses the selection of reference functions and decision thresholds, and evaluates the system's performance under various transmission systems and artificial transmission variations. The results demonstrate the system's effectiveness in speaker verification, even when there are significant differences in transmission characteristics.