Analog synthesizers, such as the modular Moog and ARP synthesizers, typically used elementary waveforms such as sawtooth, pulse train, and the like. A variety of signal models has been developed for generating such waveforms digitally without incurring the aliasing associated with simply sampling the ideal waveforms. A special issue of the IEEE Transactions on Audio, Speech, and Language Processing was devoted to this area in 2010. Specific related papers include [518,327]. The same issue also included papers on more model-based approaches in which the original analog circuit is digitized using general methods , some of which will be discussed here in later chapters. Waveform signal models will not be discussed further in this book, so see the references for further guidance in this area [518,327,326,347,506,507,479,505,480,67,78].