Fixed-Point Analysis and Parameter Selections of MSR-CORDIC With Applications to FFT Designs

• Published in: IEEE transactions on signal processing Vol. 60; no. 12; pp. 6245 - 6256
• Main Authors: Park, Sang Yoon, Yu, Ya Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithm design and analysis; Algorithms; Applied sciences; Approximation algorithms; Approximation error; Coordinate rotation digital computer (CORDIC); Detection, estimation, filtering, equalization, prediction; error analysis; Exact sciences and technology; fast Fourier transform (FFT); fixed-point; Fourier transforms; Information, signal and communications theory; mixed-scaling-rotation (MSR)-CORDIC; Optimization; Signal and communications theory; Signal processing algorithms; Signal, noise; Studies; Telecommunications and information theory; Error analysis; Error estimation; Fast Fourier transformation; Rounding error; Word length; fast Fourier transform (FFT); Algorithm; Mean square error; Coordinate rotation digital computer (CORDIC); mixed-scaling-rotation (MSR)-CORDIC; Summing circuits; fixed-point; Computer; Signal processing; Approximation error; Signal to noise ratio; Fixed point
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2012.2214218

Mixed-scaling-rotation (MSR) coordinate rotation digital computer (CORDIC) is an attractive approach to synthesizing complex rotators. This paper presents the fixed-point error analysis and parameter selections of MSR-CORDIC with applications to the fast Fourier transform (FFT). First, the fixed-point mean squared error of the MSR-CORDIC is analyzed by considering both the angle approximation error and signal round-off error incurred in the finite precision arithmetic. The signal to quantization noise ratio (SQNR) of the output of the FFT synthesized using MSR-CORDIC is thereafter estimated. Based on these analyses, two different parameter selection algorithms of MSR-CORDIC are proposed for general and dedicated MSR-CORDIC structures. The proposed algorithms minimize the number of adders and word-length when the SQNR of the FFT output is constrained. Design examples show that the FFT designed by the proposed method exhibits a lower hardware complexity than existing methods.