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Open Access Publications from the University of California

On the fixed-point analysis and architecture design of FFT algorithms

  • Author(s): Chang, Wei-Hsin
  • et al.

In this thesis, first we investigate the principle of finding the optimized coefficient set of IntFFT. IntFFT has been regarded as an approximation of original FFT computation since it utilizes lifting scheme and decomposes the complex multiplication of twiddle factor into three lifting steps. Based on the observation of the quantization loss model of lifting operations, we can select an optimized coefficient set and achieve better SQNR and reduce size of coefficient table. Secondly, we analyze the fixed-point effect of arithmetic quantization errors for different FFT algorithms. A general analytic expression is derived to quantitatively compare the overall quantization loss. An operational optimization procedure is also proposed to find the optimal memory setting for short-length FFT architecture. Last, a parallel VLSI architecture based on mixed-radix IntFFT for the upcoming MB-OFDM system is proposed. The periodicity property of lifting coefficients and the concurrent relationship of non-trivial multiplications are both utilized to reduce the hardware cost of complex multipliers

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