### Abstract

For short data sequences, Winograd's convolution algorithms attaining the minimum number of multiplications also attain a low number of additions, making them very efficient. However, for longer lengths they require a larger number of additions. Winograd's approach is usually extended to longer lengths by using a nesting approach such as the Agarwal-Cooley [1] or Split-Nesting [7] algorithms. Although these nesting algorithms are organizationally quite simple, they do not make the greatest use of the factorability of the data sequence length. The algorithm we propose adheres to Winograd's original approach more closely than do the nesting algorithms. By evaluating polynomials over simple matrices we retain, in algorithms for longer lengths, the basic structure and strategy of Winograd's approach, thereby designing computationally refined algorithms. This tactic is arithmetically profitable because Winograd's approach is based on a theory of minimum multiplicative complexity.

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

Publisher | IEEE |

Pages | 449-452 |

Number of pages | 4 |

Volume | 2 |

State | 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. 449-452). IEEE.

**Extending Winograd's small convolution algorithm to longer lengths.** / Selesnick, Ivan; Burrus, C. Sidney.

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

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 2, IEEE, pp. 449-452, Proceedings of the 1994 IEEE International Symposium on Circuits and Systems. Part 3 (of 6), London, England, 5/30/94.

}

TY - GEN

T1 - Extending Winograd's small convolution algorithm to longer lengths

AU - Selesnick, Ivan

AU - Burrus, C. Sidney

PY - 1994

Y1 - 1994

N2 - For short data sequences, Winograd's convolution algorithms attaining the minimum number of multiplications also attain a low number of additions, making them very efficient. However, for longer lengths they require a larger number of additions. Winograd's approach is usually extended to longer lengths by using a nesting approach such as the Agarwal-Cooley [1] or Split-Nesting [7] algorithms. Although these nesting algorithms are organizationally quite simple, they do not make the greatest use of the factorability of the data sequence length. The algorithm we propose adheres to Winograd's original approach more closely than do the nesting algorithms. By evaluating polynomials over simple matrices we retain, in algorithms for longer lengths, the basic structure and strategy of Winograd's approach, thereby designing computationally refined algorithms. This tactic is arithmetically profitable because Winograd's approach is based on a theory of minimum multiplicative complexity.

AB - For short data sequences, Winograd's convolution algorithms attaining the minimum number of multiplications also attain a low number of additions, making them very efficient. However, for longer lengths they require a larger number of additions. Winograd's approach is usually extended to longer lengths by using a nesting approach such as the Agarwal-Cooley [1] or Split-Nesting [7] algorithms. Although these nesting algorithms are organizationally quite simple, they do not make the greatest use of the factorability of the data sequence length. The algorithm we propose adheres to Winograd's original approach more closely than do the nesting algorithms. By evaluating polynomials over simple matrices we retain, in algorithms for longer lengths, the basic structure and strategy of Winograd's approach, thereby designing computationally refined algorithms. This tactic is arithmetically profitable because Winograd's approach is based on a theory of minimum multiplicative complexity.

UR - http://www.scopus.com/inward/record.url?scp=0028572776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028572776&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0028572776

VL - 2

SP - 449

EP - 452

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - IEEE

ER -