Comparison of signal processing methods for calculating point-by-point Discrete Fourier Transforms

This paper presents and compares signal processing architectures for calculating point-by-point discrete signal spectra. Besides the well known Discrete Fourier Transform (DFT) and its well known fast implementation, the FFT, the Sliding Discrete Fourier Transform (S-DFT) and the less known Recursive Discrete Fourier Transform (R-DFT) are discussed. These algorithms are compared by calculation complexity for FPGA implementation. Furthermore, their sensitivity to quantization effects are also examined, based on simulations.

[1]  Henk D. L. Hollmann,et al.  Implementation of "Split-radix" FFT algorithms for complex, real, and real symmetric data , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  Gábor Péceli,et al.  A common structure for recursive discrete transforms , 1986 .

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

[4]  E. Jacobsen,et al.  The sliding DFT , 2003, IEEE Signal Process. Mag..

[5]  Z. Kollar,et al.  Recursive Discrete Fourier Transform based SMT receivers for cognitive radio applications , 2012, 2012 19th International Conference on Systems, Signals and Image Processing (IWSSIP).