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A Low-Cost, Low-Complexity, and Memory-Free Architecture of Novel Recursive DFT and IDFT Algorithms for DTMF Application

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4 Author(s)
Shin-Chi Lai ; Department of Electrical Engineering, National Cheng Kung University, Tainan , Taiwan ; Sheau-Fang Lei ; Wen-Ho Juang ; Ching-Hsing Luo

A low-computational complexity and low-cost recursive discrete Fourier transform (RDFT) design using the Chinese remainder theorem is proposed in this brief. The proposed algorithm reduces multiplications by 74% and additions by 73% compared to the latest RDFT algorithms. For computing the 212- and 106-point DFT coefficients, the proposed design can shorten computing cycles by 47% compared with the latest architectures. The hardware resources for the proposed design only require 2 multipliers and 12 adders. The coefficient read-only memory storing the sine and cosine values can be reduced by 100% compared with other recursive algorithms. Therefore, the proposed algorithm is more suitable than other very large scale integration realizations.

Published in:

IEEE Transactions on Circuits and Systems II: Express Briefs  (Volume:57 ,  Issue: 9 )