CORDIC as a Switched Nonlinear System
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The COordinate Rotation DIgital Computer or CORDIC is an iterative algorithm for computing vector rotation. It uses only shift-and-add operations that make it a popular choice for computing operations such as vector rotation, matrix, trigonometric, hyperbolic, logarithmic and exponential computations in embedded platforms. This paper gives a control perspective to the algorithm by describing it as a switched autonomous nonlinear discrete system. A Lyapunov function-based analysis for switched system is applied to show the stability of the system. This analysis provides a methodology to derive metrics for comparing various variations developed for reducing latency. Further, the switching behavior is analyzed and a novel architecture is developed for reducing latency without any compromise on the metrics. The hardware implementation of novel architecture is based on the attempt to unfold the conventional architecture by predicting the switching signal.
KeywordsCORDIC FPGA Architecture Latency Stability Convergence Lyapunov Nonlinear Switched system Unfolding
- 16.K.K. Parhi, VLSI Digital Signal Processing Systems: Design and Implementation (Wiley, Hoboken, 1999)Google Scholar
- 22.Wang, S., Swartzlander, E.E. Jr.: Critically damped CORDIC algorithm. In: Proceedings of Midwest Symposium on Circuits and Systems (MWS-CAS), pp. 253–256 (1994)Google Scholar
- 23.A.G. Wills, G. Knagge, B. Ninness, Fast linear model predictive control via custom integrated circuit architecture. IEEE Trans. Control Syst. Technol. 20(1), 59–71 (2012)Google Scholar