An Arithmetic Series-Based Recursive Equation Used in the Approximation of the Sinusoidal Wave with Reduced Error

Using recursive equations (RE) to replace the traditional table lookup is beneficial to reduce the amount of data storage required for the chip design. However, the traditional cosine recursive equation (CRE) isn't suitable for being performed by digital circuits, because the digital circuit has some undesirable characteristics such as low precision for representing decimals and with significant error accumulation with the recursive process. Even an additional recursive correction is done every cycle, the associated discontinuities would incur low-frequency harmonic. In order to solve this problem, this study proposes an arithmetic series-based recursive equation (ARE), which not only improves the mentioned problems, but also makes the RE be simpler. It will speed up the calculation, refine the timing, area and power consumption, and make it possible to be applied to the chip design that requires higher frequency. To further make the recursive results be closer to the theoretical value of the sine wave/function, a recursive correction compensator (RCC) is presented. The distortion in the recursive results can thus be reduced. A comparative simulation setup is used to verify the proposed approach.