Design of digital sinusoidal oscillators with absolute periodicity

The design of digital sinusoidal oscillators with finite word lengths having excellent periodicity is proposed. The design utilizes the fundamental properties of a simple second-order difference equation containing a single multiplication coefficient. Two different design methods are outlined. In the first method, a set of values of the multiplier coefficient and the initial states are selected appropriately to guarantee periodicity after quantization. In the second method, periodicity is insured by forcing one or two selected future sample values equal to certain past sample values. Experimental results of the hardware implementation of oscillators designed using both methods are included.