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

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.