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The Performance of Look-Ahead Sigma-Delta Modulators with Unstable Noise Shaping Filters

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Look-ahead Sigma-Delta modulators look forward k samples before deciding to output a “one” or a “zero”. We look at the performance of such modulators, when used with unstable noise shaping filters, and examine the trade-off between the number of paths that must be kept alive, and the look-ahead depth needed, to assure stability. Such information helps define the number of required paths in a “Pruned Tree” algorithm or the stack size in a “Stack” algorithm, as well as the minimum search depth required. Results are presented showing that an unstable noise-shaping filter, with an out-of-band gain of 3.0, can be used successfully. This gives a 10-12 dB improvement in signal-to-noise ratio, compared to a conventional modulator.

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