Single-stage, 1-bit sigma-delta converters are in principle imperfectible. We prove this fact. The reason, simply stated, is that, when properly dithered, they are in constant overload. Prevention of overload allows only partial dithering to be performed. The consequence is that distortion, limit cycles, instability, and noise modulation can never be totally avoided. We demonstrate these effects, and using coherent averaging techniques, are able to display the consequent profusion of nonlinear artefacts which are usually hidden in the noise floor. Recording, editing, storage, or conversion systems using single-stage, 1-bit sigma-delta modulators, are thus inimical to audio of the highest quality. In contrast, multi-bit sigma-delta converters, which output linear PCM code, are in principle infinitely perfectible. (Here, multi-bit refers to at least two bits in the converter.) They can be properly dithered so as to guarantee the absence of all distortion, limit cycles, and noise modulation. The audio industry is misguided if it adopts 1-bit sigma-delta conversion as the basis for any high-quality processing, archiving, or distribution format to replace multi-bit, linear PCM.
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