The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function

The Walsh and Haar spectral transforms play a crucial part in the analysis, design, and testing of digital devices. They are most suitable for analysis and synthesis of switching or Boolean functions (BFs). It is well known that, the connection between the two spectral domains is given in terms of t...

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Main Authors:	Rafiq, Hashum M., Siddiqi, Mohammad Umar
Format:	Article
Language:	English
Published:	IJERA Publication 2016
Subjects:	TK5101 Telecommunication. Including telegraphy, radio, radar, television
Online Access:	http://irep.iium.edu.my/55591/ http://irep.iium.edu.my/55591/ http://irep.iium.edu.my/55591/1/~~%20Hashum%20~%20IJERA%20~%20HRT%20~%20Haar%20Recursive%20Transform%20~%20I0611054658.pdf

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recordtype	eprints
spelling	iium-555912017-07-19T06:41:15Z http://irep.iium.edu.my/55591/ The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function Rafiq, Hashum M. Siddiqi, Mohammad Umar TK5101 Telecommunication. Including telegraphy, radio, radar, television The Walsh and Haar spectral transforms play a crucial part in the analysis, design, and testing of digital devices. They are most suitable for analysis and synthesis of switching or Boolean functions (BFs). It is well known that, the connection between the two spectral domains is given in terms of the Walsh-Paley transform. This paper derives an alternative expression of the Walsh-Paley transform in terms of the Haar transform. The work demonstrates the possibility of obtaining both the Haar spectrum and the Walsh-Paley spectrum using only the Haar transform domain. The paper introduces a new Haar-based transform algorithm (Haar-Paley-Recursive Transform, HPRT) in the form of a recursive function along with its fast transform version. The new algorithm is then explored in its interpretation of the Walsh-Paley transform and its connection to the Autocorrelation function (ACF) of a BF. The connection is given analogously in terms of the Haar-Paley power spectrum via the Wiener-Khintchine theorem. The paper then presents the simulation results on the execution times of both derived algorithms in comparison to the existing Walsh benchmark. The work shows the advantages of using the Haar transform domain in computing the Walsh-Paley spectrum and in effect the ACF. IJERA Publication 2016-11 Article PeerReviewed application/pdf en http://irep.iium.edu.my/55591/1/~~%20Hashum%20~%20IJERA%20~%20HRT%20~%20Haar%20Recursive%20Transform%20~%20I0611054658.pdf Rafiq, Hashum M. and Siddiqi, Mohammad Umar (2016) The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function. International Journal of Engineering Research and Application ( IJERA ), 6 (11). pp. 46-58. ISSN 2248-9622 http://www.ijera.com
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	TK5101 Telecommunication. Including telegraphy, radio, radar, television
spellingShingle	TK5101 Telecommunication. Including telegraphy, radio, radar, television Rafiq, Hashum M. Siddiqi, Mohammad Umar The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
description	The Walsh and Haar spectral transforms play a crucial part in the analysis, design, and testing of digital devices. They are most suitable for analysis and synthesis of switching or Boolean functions (BFs). It is well known that, the connection between the two spectral domains is given in terms of the Walsh-Paley transform. This paper derives an alternative expression of the Walsh-Paley transform in terms of the Haar transform. The work demonstrates the possibility of obtaining both the Haar spectrum and the Walsh-Paley spectrum using only the Haar transform domain. The paper introduces a new Haar-based transform algorithm (Haar-Paley-Recursive Transform, HPRT) in the form of a recursive function along with its fast transform version. The new algorithm is then explored in its interpretation of the Walsh-Paley transform and its connection to the Autocorrelation function (ACF) of a BF. The connection is given analogously in terms of the Haar-Paley power spectrum via the Wiener-Khintchine theorem. The paper then presents the simulation results on the execution times of both derived algorithms in comparison to the existing Walsh benchmark. The work shows the advantages of using the Haar transform domain in computing the Walsh-Paley spectrum and in effect the ACF.
format	Article
author	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_facet	Rafiq, Hashum M. Siddiqi, Mohammad Umar
author_sort	Rafiq, Hashum M.
title	The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
title_short	The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
title_full	The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
title_fullStr	The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
title_full_unstemmed	The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function
title_sort	haar-recursive transform and its consequence to the walsh-paley spectrum and the autocorrelation function
publisher	IJERA Publication
publishDate	2016
url	http://irep.iium.edu.my/55591/ http://irep.iium.edu.my/55591/ http://irep.iium.edu.my/55591/1/~~%20Hashum%20~%20IJERA%20~%20HRT%20~%20Haar%20Recursive%20Transform%20~%20I0611054658.pdf
first_indexed	2023-09-18T21:18:33Z
last_indexed	2023-09-18T21:18:33Z
_version_	1777411727115157504

The Haar-Recursive transform and its consequence to the Walsh-paley spectrum and the autocorrelation function

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