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The Harmonic Content of a Limit Cycle in a DSD Bitstream

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This work explores the effects of limit cycles on the frequency content in the DSD bitstream. We show how any periodic bitstream can be expressed as a sum of square waves of various phases with width equal to the sampling period. A Fourier expansion may be used to exactly determine the phases and amplitudes of all spectral content. We thus determine all harmonics that appear in the output, and thus are able to distinguish limit cycles from idle tones. These results are put into the context of recent advances in the theory of limit cycles and idle tones in sigma delta modulators.

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