The Fast Walsh-Hadamard Transform and Processors by Using Delay Lines

Mikio NAKATSUYAMA; Norio NISHIZUKA

The Fast Walsh-Hadamard Transform and Processors by Using Delay Lines

Mikio NAKATSUYAMA, Norio NISHIZUKA

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The algorithm for the fast Walsh-Hadamard transform (FWT) derived from the Walsh-Paley function provides fast and simple processors which calculate the i-th Walsh transform F_i (i0, 1, , 2ⁿ1) of the natural-, dyadic-, and sequency-ordered Walsh-Hadamard transforms respectively according to control signals. This processor needs only 2・2ⁿ1 adder-subtractors (A/S) and is n times as fast as the one of the iterative type with n iterations. The characteristics of FWT with the term T resemble that of the assembly of digital filters. The digital filter representing FWT can be analyzed with z-transform and its transfer function is described as a simple function of z. The 3 dB bandwidth calculated by FWT is almost constant (about 0.85/T) for n2, 3, ...,10. All the Walsh transform F_i can be calculated by the processor with n・2ⁿ A/S, while the processor using delay lines needs only 2・2ⁿ1 A/S. The improved processor with delay lines deals with successive data and calculates all the Walsh transform or the Walsh spectrograms at the same time. These processors are effective for the recognition of speech and the analysis of signals.

Publication: IEICE TRANSACTIONS on transactions Vol.E64-E No.11 pp.708-715

Publication Date: 1981/11/25

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Type of Manuscript: PAPER

Category: Data Processing

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Mikio NAKATSUYAMA
Norio NISHIZUKA

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Mikio NAKATSUYAMA, Norio NISHIZUKA, "The Fast Walsh-Hadamard Transform and Processors by Using Delay Lines" in IEICE TRANSACTIONS on transactions, vol. E64-E, no. 11, pp. 708-715, November 1981, doi: .
Abstract: The algorithm for the fast Walsh-Hadamard transform (FWT) derived from the Walsh-Paley function provides fast and simple processors which calculate the i-th Walsh transform F_i (i0, 1, , 2ⁿ1) of the natural-, dyadic-, and sequency-ordered Walsh-Hadamard transforms respectively according to control signals. This processor needs only 2・2ⁿ1 adder-subtractors (A/S) and is n times as fast as the one of the iterative type with n iterations. The characteristics of FWT with the term T resemble that of the assembly of digital filters. The digital filter representing FWT can be analyzed with z-transform and its transfer function is described as a simple function of z. The 3 dB bandwidth calculated by FWT is almost constant (about 0.85/T) for n2, 3, ...,10. All the Walsh transform F_i can be calculated by the processor with n・2ⁿ A/S, while the processor using delay lines needs only 2・2ⁿ1 A/S. The improved processor with delay lines deals with successive data and calculates all the Walsh transform or the Walsh spectrograms at the same time. These processors are effective for the recognition of speech and the analysis of signals.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e64-e_11_708/_p

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@ARTICLE{e64-e_11_708,
author={Mikio NAKATSUYAMA, Norio NISHIZUKA, },
journal={IEICE TRANSACTIONS on transactions},
title={The Fast Walsh-Hadamard Transform and Processors by Using Delay Lines},
year={1981},
volume={E64-E},
number={11},
pages={708-715},
abstract={The algorithm for the fast Walsh-Hadamard transform (FWT) derived from the Walsh-Paley function provides fast and simple processors which calculate the i-th Walsh transform F_i (i0, 1, , 2ⁿ1) of the natural-, dyadic-, and sequency-ordered Walsh-Hadamard transforms respectively according to control signals. This processor needs only 2・2ⁿ1 adder-subtractors (A/S) and is n times as fast as the one of the iterative type with n iterations. The characteristics of FWT with the term T resemble that of the assembly of digital filters. The digital filter representing FWT can be analyzed with z-transform and its transfer function is described as a simple function of z. The 3 dB bandwidth calculated by FWT is almost constant (about 0.85/T) for n2, 3, ...,10. All the Walsh transform F_i can be calculated by the processor with n・2ⁿ A/S, while the processor using delay lines needs only 2・2ⁿ1 A/S. The improved processor with delay lines deals with successive data and calculates all the Walsh transform or the Walsh spectrograms at the same time. These processors are effective for the recognition of speech and the analysis of signals.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - The Fast Walsh-Hadamard Transform and Processors by Using Delay Lines
T2 - IEICE TRANSACTIONS on transactions
SP - 708
EP - 715
AU - Mikio NAKATSUYAMA
AU - Norio NISHIZUKA
PY - 1981
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E64-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1981
AB - The algorithm for the fast Walsh-Hadamard transform (FWT) derived from the Walsh-Paley function provides fast and simple processors which calculate the i-th Walsh transform F_i (i0, 1, , 2ⁿ1) of the natural-, dyadic-, and sequency-ordered Walsh-Hadamard transforms respectively according to control signals. This processor needs only 2・2ⁿ1 adder-subtractors (A/S) and is n times as fast as the one of the iterative type with n iterations. The characteristics of FWT with the term T resemble that of the assembly of digital filters. The digital filter representing FWT can be analyzed with z-transform and its transfer function is described as a simple function of z. The 3 dB bandwidth calculated by FWT is almost constant (about 0.85/T) for n2, 3, ...,10. All the Walsh transform F_i can be calculated by the processor with n・2ⁿ A/S, while the processor using delay lines needs only 2・2ⁿ1 A/S. The improved processor with delay lines deals with successive data and calculates all the Walsh transform or the Walsh spectrograms at the same time. These processors are effective for the recognition of speech and the analysis of signals.
ER -