A theoretical basis is provided for multistage sigma-delta modulation (MSM), which is a cascade realization of several single-loop sigma-delta modulators with a linear combinatorial network. Equations are derived describing the output and the quantization noise of MSM for an arbitrary input signal, and the noise-shaping characteristic of MSM is investigated. The spectral characteristics of an m-stage sigma-delta modulator with both DC and sinusoidal inputs are developed. For both types of inputs the binary quantizer noise of the mth (m>or=3) quantizer, which appears at the output as an mth order difference, is asymptotically white, uniformly distributed, and uncorrelated with the input level. It is also found that for an m-stage sigma-delta quantizer with either an ideal low-pass filter or a sinc/sup m+1/ filter decoder, the average quantization noise of the system is inversely proportional to the (2m+1)th power of the oversampling ratio. This implies that the high-order systems are favourable in terms of the trade-off between the quantization noise and oversampling ratio. Simulation results are presented to support the theoretical analysis. >