### Abstract

A new DFT computation method based on a subband decomposition is outlined for one- and two-dimensional (2-D) real-valued finite-length sequences. The two distinct parts of the algorithm, a preprocessing Hadamard-transform stage and a 'correction' stage are interpreted as a filter bank plus a recombination network, and are compared to the corresponding filter bank interpretation of the direct DFT and the classical FFT algorithms. The preprocessing stage decomposes the original sequence into a set of smaller length subsequences approximately separated in the spectral domain. The overall DFT is then given by a weighted sum of smaller length DFTs with the weights determined by the recombination network. The frequency-separation property of the subsequences permits elimination of the subsequences with negligible energy contribution from the DFT calculation thus resulting in a fast approximate DFT computation method. Various implementation schemes for the subband DFT computation method are outlined. As a first extension, adaptive versions are described, finding the band(s) of interest automatically. Furthermore, a generalized preprocessing stage as well as the extension to the 2-D case are addressed.

Original language | English |
---|---|

Pages (from-to) | 261-277 |

Number of pages | 17 |

Journal | Signal Processing |

Volume | 41 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 |

### Fingerprint

### Keywords

- Adaptive FFT
- Approximate DFT computation
- Discrete Fourier transform
- Spectral analysis
- Subband FFT

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition
- Signal Processing
- Software
- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Signal Processing*,

*41*(3), 261-277. https://doi.org/10.1016/0165-1684(94)00103-7

**Subband DFT - Part I : Definition, interpretation and extensions.** / Shentov, O. V.; Mitra, S. K.; Heute, U.; Hossen, A. N.

Research output: Contribution to journal › Article

*Signal Processing*, vol. 41, no. 3, pp. 261-277. https://doi.org/10.1016/0165-1684(94)00103-7

}

TY - JOUR

T1 - Subband DFT - Part I

T2 - Definition, interpretation and extensions

AU - Shentov, O. V.

AU - Mitra, S. K.

AU - Heute, U.

AU - Hossen, A. N.

PY - 1995

Y1 - 1995

N2 - A new DFT computation method based on a subband decomposition is outlined for one- and two-dimensional (2-D) real-valued finite-length sequences. The two distinct parts of the algorithm, a preprocessing Hadamard-transform stage and a 'correction' stage are interpreted as a filter bank plus a recombination network, and are compared to the corresponding filter bank interpretation of the direct DFT and the classical FFT algorithms. The preprocessing stage decomposes the original sequence into a set of smaller length subsequences approximately separated in the spectral domain. The overall DFT is then given by a weighted sum of smaller length DFTs with the weights determined by the recombination network. The frequency-separation property of the subsequences permits elimination of the subsequences with negligible energy contribution from the DFT calculation thus resulting in a fast approximate DFT computation method. Various implementation schemes for the subband DFT computation method are outlined. As a first extension, adaptive versions are described, finding the band(s) of interest automatically. Furthermore, a generalized preprocessing stage as well as the extension to the 2-D case are addressed.

AB - A new DFT computation method based on a subband decomposition is outlined for one- and two-dimensional (2-D) real-valued finite-length sequences. The two distinct parts of the algorithm, a preprocessing Hadamard-transform stage and a 'correction' stage are interpreted as a filter bank plus a recombination network, and are compared to the corresponding filter bank interpretation of the direct DFT and the classical FFT algorithms. The preprocessing stage decomposes the original sequence into a set of smaller length subsequences approximately separated in the spectral domain. The overall DFT is then given by a weighted sum of smaller length DFTs with the weights determined by the recombination network. The frequency-separation property of the subsequences permits elimination of the subsequences with negligible energy contribution from the DFT calculation thus resulting in a fast approximate DFT computation method. Various implementation schemes for the subband DFT computation method are outlined. As a first extension, adaptive versions are described, finding the band(s) of interest automatically. Furthermore, a generalized preprocessing stage as well as the extension to the 2-D case are addressed.

KW - Adaptive FFT

KW - Approximate DFT computation

KW - Discrete Fourier transform

KW - Spectral analysis

KW - Subband FFT

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UR - http://www.scopus.com/inward/citedby.url?scp=0029253689&partnerID=8YFLogxK

U2 - 10.1016/0165-1684(94)00103-7

DO - 10.1016/0165-1684(94)00103-7

M3 - Article

AN - SCOPUS:0029253689

VL - 41

SP - 261

EP - 277

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

IS - 3

ER -