CORDIC based implementation of Fast Fourier Transform

CORDIC is an iterative arithmetic computing algorithm capable of evaluating various elementary functions using a unified shift-and-add operations. Fast Fourier Transform processor based on CORDIC is implemented. The key ideas are replacing the sine and cosine twiddle factors in conventional FFT architecture by iterative CORDIC rotations which allow the reduction in read-only memory (ROM). The use of CORDIC in FFT results in the elimination of multipliers, saves area, power and cost CORDIC finds many applications as it providing a simpler way of computing complex multiplications. It is proved that CORDIC is most suitable alternative.

[1]  K. Sridharan,et al.  50 Years of CORDIC: Algorithms, Architectures, and Applications , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Jean-Michel Muller,et al.  Elementary Functions: Algorithms and Implementation , 1997 .

[3]  Behrooz Parhami,et al.  Computer arithmetic - algorithms and hardware designs , 1999 .

[4]  Jean-Michel Muller,et al.  The CORDIC Algorithm: New Results for Fast VLSI Implementation , 1993, IEEE Trans. Computers.

[5]  Y.H. Hu,et al.  CORDIC-based VLSI architectures for digital signal processing , 1992, IEEE Signal Processing Magazine.

[6]  José Francisco López,et al.  A CORDIC processor for FFT computation and its implementation using gallium arsenide technology , 1998, IEEE Trans. Very Large Scale Integr. Syst..

[7]  S. Walther.  A unified algorithm for elementary functions , 1899 .

[8]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[9]  Jayshankar.  Efficient computation of the DFT of a 2N - point real sequence using FFT with CORDIC based butterflies , 2008, TENCON 2008 - 2008 IEEE Region 10 Conference.

[10]  Alvin M. Despain,et al.  Fourier Transform Computers Using CORDIC Iterations , 1974, IEEE Transactions on Computers.

[11]  Jack E. Volder,et al.  The CORDIC computing technique , 1899, IRE-AIEE-ACM '59 (Western).

[12]  Earl E. Swartzlander,et al.  Hybrid CORDIC Algorithms , 1997, IEEE Trans. Computers.

[13]  Alan R. Jones,et al.  Fast Fourier Transform , 1970, SIGP.

[14]  Shen-Fu Hsiao,et al.  Householder CORDIC Algorithms , 1995, IEEE Trans. Computers.

[15]  Ray Andraka,et al.  A survey of CORDIC algorithms for FPGA based computers , 1998, FPGA '98.

[16]  Steven G. Johnson,et al.  A Modified Split-Radix FFT With Fewer Arithmetic Operations , 2007, IEEE Transactions on Signal Processing.

[17]  Heinrich Meyr,et al.  The Differential CORDIC Algorithm: Constant Scale Factor Redundant Implementation without Correcting Iterations , 1996, IEEE Trans. Computers.

[18]  Earl E. Swartzlander,et al.  Implementation of a single chip, pipelined, complex, one-dimensional fast Fourier transform in 0.25 /spl mu/m bulk CMOS , 2002, Proceedings IEEE International Conference on Application- Specific Systems, Architectures, and Processors.

[19]  Jack E. Volder.  The CORDIC Trigonometric Computing Technique , 1959, IRE Trans. Electron. Comput..