The Two-Dimensional Lapped Hadamard Transform

Shogo MURAMATSU; Akihiko YAMADA; Hitoshi KIYA

The Two-Dimensional Lapped Hadamard Transform

Shogo MURAMATSU, Akihiko YAMADA, Hitoshi KIYA

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In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.8 pp.1542-1549

Publication Date: 1998/08/25

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Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)

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Shogo MURAMATSU, Akihiko YAMADA, Hitoshi KIYA, "The Two-Dimensional Lapped Hadamard Transform" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 8, pp. 1542-1549, August 1998, doi: .
Abstract: In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_8_1542/_p

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@ARTICLE{e81-a_8_1542,
author={Shogo MURAMATSU, Akihiko YAMADA, Hitoshi KIYA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Two-Dimensional Lapped Hadamard Transform},
year={1998},
volume={E81-A},
number={8},
pages={1542-1549},
abstract={In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - The Two-Dimensional Lapped Hadamard Transform
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1542
EP - 1549
AU - Shogo MURAMATSU
AU - Akihiko YAMADA
AU - Hitoshi KIYA
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1998
AB - In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.
ER -