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This paper considers interleaved, multichannel measurements as arise for example in time-interleaved analog-to-digital (A/D) converters and in distributed sensor networks. Such systems take the form of either uniform or recurrent nonuniform sampling, depending on the relative timing between the channels. Uniform (i.e., linear) quantization in each channel results in an effective overall signal-to-quantization-error ratio (SQNR) in the reconstructed output which is dependent on the quantizer step size in each channel, the relative timing between the channels, and the oversampling ratio. It is shown that in the multichannel sampling system when the quantization step size is not restricted to be the same in each channel and the channel timing is not constrained to correspond to uniform sampling, it is often possible to increase the SQNR relative to the uniform case. Appropriate choice of these parameters together with the design of appropriate compensation filtering is developed.