Modulo sigma-delta modulation

A modulo sigma-delta modulator is introduced, and the behavior of the quantization error is derived. The system consists of a modulo limiter followed by a sigma-delta modulator. The limiter confines the input to the no-overload region of the sigma-delta modulator, and the modulo arithmetic performed by the limiter is amenable to recently developed techniques for the exact analysis of quantizer error behavior in sigma-modulators with bounded inputs. The quantization error behavior is derived for a modulator driven by a quasi-stationary random process. The limit distribution and the power of the quantization error are found. Except for some singular cases, the normalized quantization error is uniformly distributed in (-1/2, 1/2). The power spectrum and the autocorrelation function of the quantization error with a causal ARMA (p, q) process input are also derived. It is shown that the quantization noise is white when the input is a random process with stationary independent increments. Simulation results support the theoretical analysis. >

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