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The precoder-equalizer system considered by X.G. Xia (1997) is analyzed using periodic nonuniform sampling theorem. The ISI channel is modeled as multiband channels with different spectral supports, and the channel output are periodic nonuniform sampled. We discussed the necessary and sufficient conditions of the channel and the sampling rate that allows ISI free communication. A characterization and parameterization of the precoder are derived, which can be used to construct power optimized precoders and minimum channel noise power amplification equalizers.