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This book describes several Digital Delta-Sigma Modulator (DDSM) architectures, including multi stage noise shaping (MASH), error feedback modulator (EFM) and single quantizer (SQ)-DDSM modulators, with a focus on predicting and maximizing their cycle lengths. The authors aim to demystify an important aspect of these particular DDSM structures, namely the existence of spurs resulting from the inherent periodicity of DDSMs with constant inputs. Simulink and MATLAB models and code are presented in Chapters 2-5 to enable the reader to reproduce the results in this work and to explore further. These examples will also be helpful for first-time designers of DDSMs.