Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms

C. Radhakrishnan; W. K. Jenkins

doi:10.1109/ACSSC.2011.6189974

Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms

C. Radhakrishnan, W. K. Jenkins

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

2 Scopus citations

Abstract

Recently the Modified Fermat Number Transform (MFNT) was extended to a Quadratic MFNT (QMFNT) by combining Right Circular Convolution (RCC) and Left Circular Convolution (LCC) to produce a quadratic representation of the convolution output. This paper investigates nesting of two distinct quadratic number representations, the first associated with quadratic coding of complex input sequences, and the second associated with QMFNT block processing. Quadratic coding of complex sequences combined with QMFNT block processing eliminates cross-products in the complex multiplication. Finally, a generalized form of the QMFNT (GMFNT) is introduced and then extended into two dimensions.

Original language	English (US)
Title of host publication	Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
Pages	149-153
Number of pages	5
DOIs	https://doi.org/10.1109/ACSSC.2011.6189974
State	Published - 2011
Event	45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011 - Pacific Grove, CA, United States Duration: Nov 6 2011 → Nov 9 2011

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)	1058-6393

Other

Other	45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
Country/Territory	United States
City	Pacific Grove, CA
Period	11/6/11 → 11/9/11

All Science Journal Classification (ASJC) codes

Signal Processing
Computer Networks and Communications

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10.1109/ACSSC.2011.6189974

Cite this

Radhakrishnan, C., & Jenkins, W. K. (2011). Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms. In Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011 (pp. 149-153). Article 6189974 (Conference Record - Asilomar Conference on Signals, Systems and Computers). https://doi.org/10.1109/ACSSC.2011.6189974

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title = "Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms",

abstract = "Recently the Modified Fermat Number Transform (MFNT) was extended to a Quadratic MFNT (QMFNT) by combining Right Circular Convolution (RCC) and Left Circular Convolution (LCC) to produce a quadratic representation of the convolution output. This paper investigates nesting of two distinct quadratic number representations, the first associated with quadratic coding of complex input sequences, and the second associated with QMFNT block processing. Quadratic coding of complex sequences combined with QMFNT block processing eliminates cross-products in the complex multiplication. Finally, a generalized form of the QMFNT (GMFNT) is introduced and then extended into two dimensions.",

author = "C. Radhakrishnan and Jenkins, {W. K.}",

year = "2011",

doi = "10.1109/ACSSC.2011.6189974",

language = "English (US)",

isbn = "9781467303231",

series = "Conference Record - Asilomar Conference on Signals, Systems and Computers",

pages = "149--153",

booktitle = "Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011",

note = "45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011 ; Conference date: 06-11-2011 Through 09-11-2011",

}

Radhakrishnan, C & Jenkins, WK 2011, Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms. in Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011., 6189974, Conference Record - Asilomar Conference on Signals, Systems and Computers, pp. 149-153, 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011, Pacific Grove, CA, United States, 11/6/11. https://doi.org/10.1109/ACSSC.2011.6189974

Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms. / Radhakrishnan, C.; Jenkins, W. K.
Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011. 2011. p. 149-153 6189974 (Conference Record - Asilomar Conference on Signals, Systems and Computers).

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

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AB - Recently the Modified Fermat Number Transform (MFNT) was extended to a Quadratic MFNT (QMFNT) by combining Right Circular Convolution (RCC) and Left Circular Convolution (LCC) to produce a quadratic representation of the convolution output. This paper investigates nesting of two distinct quadratic number representations, the first associated with quadratic coding of complex input sequences, and the second associated with QMFNT block processing. Quadratic coding of complex sequences combined with QMFNT block processing eliminates cross-products in the complex multiplication. Finally, a generalized form of the QMFNT (GMFNT) is introduced and then extended into two dimensions.

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Radhakrishnan C, Jenkins WK. Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms. In Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011. 2011. p. 149-153. 6189974. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/ACSSC.2011.6189974

Nested quadratic arithmetic for efficient convolution of complex sequences with quadratic modified fermat number transforms

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