A psychoacoustically optimal sigma-delta modulator (SDM) possesses a noise floor with a power spectral density that is invariant with input signal characteristics, and is also minimally audible. While idle tones and noise modulation in sigma-delta modulators can be eliminated by using dither or by making the modulator chaotic, the noise floor attributable to an SDM can be made minimally audible by forcing the noise-shaping characteristic to follow the threshold of hearing. Such an action is possible in higher-order SDMs by appropriate control of noise shaping zero locations, and for a given perceived resolution, has the potential benefit of reduced oversampling factor and/or modulator order. In this paper, optimal zero locations and associated reductions in oversampling factor/modulator order are determined for SDM orders ranging from 2 and 5.
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