Research On Sampling And Reconstruction In Interleaved Multi-channel Signals

In recent years, along with the development of the computer and the VlSI circuits, the use of digitalsignal processing technology is becoming more and more widely. Time-interleaved analog-to-digitalconverters are often employed to sample high bandwidth signals or to achieve a large oversampling ratio;traditionally, the relative time delays between channels have been selected to form an overall uniformsampling pattern, with equal quantization granularity in each channel. In recent years, high bandwidthsignals or use of large oversampling ratios often require the use of time-interleaved analog-to-digitalconverters. However，sampling and quantization for optimal reconstruction has also been extensivelyresearched.Based on the current research status of reconstruction, this paper analyzes the multi-channel samplingand reconstruction of the basic knowledge, this paper develops two reconstruction methods fromnonuniform sampling. The main work of this paper is as follows:Firstly, this paper considers the environment of interleaved multi-channel measurements, and suchsystems take the form of either uniform or recurrent non-uniform sampling, depending on the relativetiming between the channels. Uniform quantization in each channel results in an effective overall SQNR(signal-to-quantization-error ratio) in the reconstructed output which is dependent on the quantizer step sizein each channel, the relative timing between the channels, and the oversampling ratio. It is shown that in theenvironment of interleaved multi-channel measurements, the quantization step size is not restricted to beidentical in each channel; or the channel timing is not constrained to correspond to uniform sampling,reconstruction of the continuous-time signal from nonuniform samples is more difficult than from uniformsamples.Secondly, this paper considered the environment of interleaved multi-channel measurements and thedesign of the optimal reconstruction filter. This paper develops a class of approximate reconstructiommethods from nonniform based on the MMSE (mean squared reconstruction error). Secondly this paperconsiders two cases. The first case is uniform sampling and designing of the optimal filters; the second caseis non-uniform, then choose the optimal time offsets where the filters are constrained, and correspond to recurrent non-uniform sampling.