Twiddle Factor Generation Using Chebyshev Polynomials and HDL for Frequency Domain Beamforming

  • Ghattas AkkadEmail author
  • Ali Mansour
  • Bachar ElHassan
  • Frederic Le Roy
  • Mohamad Najem
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 573)


Twiddle factor generation is considered a computationally intensive task in generic length, high resolution, FFT operations. In order to accelerate twiddle factor generation, we propose a reconfigurable hardware architecture based on Chebyshev polynomial expansion for computing the cosine and sine trigonometric functions under finite precision arithmetic. We show that our approach presents a flexible 3 decimal digits precision output for variable length FFT operations, since the same design space can be used for any power of 2 FFT length. In particular, this study focuses on communication systems incorporating frequency domain beamforming algorithms for single and multi-beams. The proposed architecture is competitive with classical designs i.e. Coordinate Rotation Digital Computer, CORDIC and Taylor Series by providing low latency, high precision twiddle factors for variable length FFT.


FFT FPGA Accelerated computing VHDL Beamforming Twiddle factor Chebyshev Frequency domain 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ghattas Akkad
    • 1
    • 2
    Email author
  • Ali Mansour
    • 1
  • Bachar ElHassan
    • 3
  • Frederic Le Roy
    • 1
  • Mohamad Najem
    • 4
  1. 1.Lab-STICCCNRS, UMR 6285, ENSTA BretagneBrestFrance
  2. 2.Department of Electrical EngineeringUniversity of BalamandKouraLebanon
  3. 3.Faculty of EngineeringLebanese UniversityTripoliLebanon
  4. 4.Computer and Communication EngineeringLebanese International UniversityMount LebanonLebanon

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