Abstract

Disclosed are signal generators for developing multilevel output signal sequences of a preselected period of repetition. In their general form, the generators comprise a shift register capable of storing multilevel signals, and feedback means. The feedback means multiply the output signal of prescribed shift register stages by selected integers, add the multiplied signals in nonmodulo arithmetic, and apply the added signals to the first stage of the shift register. The multiplying integers within the feedback means are selected to cause the characteristic functions of the signal generator to be a cyclotomic polynomial. For descriptive convenience, the disclosed generator is termed a "cyclotomic circuit." The disclosed cyclotomic circuits are particularly useful in a minimum memory, prescribed-period, signal generator applications. The minimum memory is achieved by separating the prescribed period into power-of-prime factors, and by associating with each factor a cyclotomic circuit. Each cyclotomic circuit develops a subsequence signal of a period equal to the power-of-prime factor, and the subsequence signals are combined in a transversal network, responsive to the cyclotomic circuits, to form the desired prescribed period sequence signal. Advantageously, the multiplying feedback integers of cyclotomic circuits of power-of-prime periods are limited to 0, 1, and -1.