### Abstract

The two main parts of the subband FFT presented recently [1],[2], a preprocessing Hadamard-transform stage and a 'correction' stage, are interpreted as a filter-bank-plus-recombination network. This interpretation is now studied in detail in terms of different filters' impulse responses in full-band and partial-band cases. The approach to a fix-point error analysis as known for, e.g., the radix-2 decimation-in-time Cooley-Tukey (CT-) FFT [3],[4] is applied to the SB-FFT. A comparison between the two FFT's is given for the full-band case. The effect of coefficient errors on the zero-pattern of the filter-bank is explained. A new measure for the coefficient error is introduced. According to this measure, the coefficient error in a channel k can be described by adding the linear distortion in this channel to the sum of the aliasing effects of all other channels on channel k. In a partial-band case, the approximation errors inherent in the SB-FFT combine with the coefficient error; this is described in a recursive form and explained by means of a numerical example for a simulated case.

Original language | English |
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Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Publisher | IEEE |

Pages | 345-348 |

Number of pages | 4 |

Volume | 2 |

Publication status | Published - 1994 |

Event | Proceedings of the 1994 IEEE International Symposium on Circuits and Systems. Part 3 (of 6) - London, England Duration: May 30 1994 → Jun 2 1994 |

### Other

Other | Proceedings of the 1994 IEEE International Symposium on Circuits and Systems. Part 3 (of 6) |
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City | London, England |

Period | 5/30/94 → 6/2/94 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(Vol. 2, pp. 345-348). IEEE.

**Filter-bank interpretation and fixed-point numerical accuracy of subband FFT.** / Heute, Ulrich; Hossen, Abdulnasir.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 2, IEEE, pp. 345-348, Proceedings of the 1994 IEEE International Symposium on Circuits and Systems. Part 3 (of 6), London, England, 5/30/94.

}

TY - GEN

T1 - Filter-bank interpretation and fixed-point numerical accuracy of subband FFT

AU - Heute, Ulrich

AU - Hossen, Abdulnasir

PY - 1994

Y1 - 1994

N2 - The two main parts of the subband FFT presented recently [1],[2], a preprocessing Hadamard-transform stage and a 'correction' stage, are interpreted as a filter-bank-plus-recombination network. This interpretation is now studied in detail in terms of different filters' impulse responses in full-band and partial-band cases. The approach to a fix-point error analysis as known for, e.g., the radix-2 decimation-in-time Cooley-Tukey (CT-) FFT [3],[4] is applied to the SB-FFT. A comparison between the two FFT's is given for the full-band case. The effect of coefficient errors on the zero-pattern of the filter-bank is explained. A new measure for the coefficient error is introduced. According to this measure, the coefficient error in a channel k can be described by adding the linear distortion in this channel to the sum of the aliasing effects of all other channels on channel k. In a partial-band case, the approximation errors inherent in the SB-FFT combine with the coefficient error; this is described in a recursive form and explained by means of a numerical example for a simulated case.

AB - The two main parts of the subband FFT presented recently [1],[2], a preprocessing Hadamard-transform stage and a 'correction' stage, are interpreted as a filter-bank-plus-recombination network. This interpretation is now studied in detail in terms of different filters' impulse responses in full-band and partial-band cases. The approach to a fix-point error analysis as known for, e.g., the radix-2 decimation-in-time Cooley-Tukey (CT-) FFT [3],[4] is applied to the SB-FFT. A comparison between the two FFT's is given for the full-band case. The effect of coefficient errors on the zero-pattern of the filter-bank is explained. A new measure for the coefficient error is introduced. According to this measure, the coefficient error in a channel k can be described by adding the linear distortion in this channel to the sum of the aliasing effects of all other channels on channel k. In a partial-band case, the approximation errors inherent in the SB-FFT combine with the coefficient error; this is described in a recursive form and explained by means of a numerical example for a simulated case.

UR - http://www.scopus.com/inward/record.url?scp=0028586296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028586296&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 345

EP - 348

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - IEEE

ER -