Digital Delta-Sigma Modulators (DDSMs) are widely used in frequency synthesizers and oversampled digital-to-analog converters. In fact, they are more widely used commercially that their analog counterparts.  This book describes several  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. Provides a clear explanation of the cause of spurious tones in digital delta-sigma modulators;  Includes formulae to predict the positions of spurious tones; Describes sample architectures to remove spurious tones; Presents Simulink and Matlab code to reproduce the examples in the book.  .