Moment-based fast discrete Hartley transform

J. G. Liu; F. H.Y. Chan; F. K. Lam; H. F. Li; George S.K. Fung

doi:10.1016/S0165-1684(03)00091-4

Moment-based fast discrete Hartley transform

J. G. Liu, F. H.Y. Chan, F. K. Lam, H. F. Li, George S.K. Fung

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying our earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(Nlog₂N/log₂log₂N) and is superior to the O(Nlog₂N) in the classical FHT. The execution time of the systolic array is only O(Nlog₂N/log₂log₂N) for one-dimensional DHT and O(N^k) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.

Original language	English (US)
Pages (from-to)	1749-1757
Number of pages	9
Journal	Signal Processing
Volume	83
Issue number	8
DOIs	https://doi.org/10.1016/S0165-1684(03)00091-4
State	Published - Aug 2003
Externally published	Yes

Keywords

Discrete Hartley transform
Fast transform
Moment
Systolic array

ASJC Scopus subject areas

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

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10.1016/S0165-1684(03)00091-4

Cite this

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title = "Moment-based fast discrete Hartley transform",

abstract = "A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying our earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(Nlog2N/log2log2N) and is superior to the O(Nlog2N) in the classical FHT. The execution time of the systolic array is only O(Nlog2N/log2log2N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.",

keywords = "Discrete Hartley transform, Fast transform, Moment, Systolic array",

author = "Liu, {J. G.} and Chan, {F. H.Y.} and Lam, {F. K.} and Li, {H. F.} and Fung, {George S.K.}",

note = "Funding Information: This research reported here is partly supported by National Natural Science Foundation of China under grant 69775011 and University of Hong Kong research grants. ",

year = "2003",

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T1 - Moment-based fast discrete Hartley transform

AU - Liu, J. G.

AU - Chan, F. H.Y.

AU - Lam, F. K.

AU - Li, H. F.

AU - Fung, George S.K.

N1 - Funding Information: This research reported here is partly supported by National Natural Science Foundation of China under grant 69775011 and University of Hong Kong research grants.

PY - 2003/8

Y1 - 2003/8

N2 - A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying our earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(Nlog2N/log2log2N) and is superior to the O(Nlog2N) in the classical FHT. The execution time of the systolic array is only O(Nlog2N/log2log2N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.

AB - A novel approach to compute the discrete Hartley transform (DHT) is proposed. By using a modular mapping, DHT is approximated by the sum of a finite sequence of discrete moments. This enables the computational techniques developed for computing moments to be employed in computing DHT efficiently. We demonstrate this by applying our earlier systolic solution for computation of discrete moments to DHT. The resulting solution has a superior complexity: the amount of multiplications used in our method is O(Nlog2N/log2log2N) and is superior to the O(Nlog2N) in the classical FHT. The execution time of the systolic array is only O(Nlog2N/log2log2N) for one-dimensional DHT and O(Nk) for k-dimensional DHT(k ≥ 2). The method is also applicable to DHT inverses.

KW - Discrete Hartley transform

KW - Fast transform

KW - Moment

KW - Systolic array

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JO - Signal Processing

JF - Signal Processing

IS - 8

ER -

Moment-based fast discrete Hartley transform

Abstract

Keywords

ASJC Scopus subject areas

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