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The Viterbi algorithm has been proposed for the symbol-by-symbol detection of discrete pulse amplitude modulated signals transmitted over noisy time-dispersive channels. The resulting detector has considerable complexity, requiring the storage of state variables for binary signaling. A truncated-state detector assumes the channel memory is much less than it really is and as such neglects some of the channel's intersymbol interference. An upper bound is prescribed for the detector's bit error probability due to this neglected interference in the case of binary signaling. This interference degrades the detector's performance in the same functional manner that intersymbol interference degrades the performance of the standard quantizing detector. This degradation can be considerably reduced for troublesome channels by optimally choosing the state variables for truncated-state detection.