The Number Theoretic Hilbert Transform

This paper presents a general expression for a number theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform matrix together with alternating values in each row being zero and non-zero. Specific examples for 4-, 6-, and 8-point NHT are...

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Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 33; no. 8; pp. 2539 - 2548
Main Author Kak, Subhash
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2014
Springer Nature B.V
Subjects
Circuits
Circuits and Systems
Cryptography
Electrical Engineering
Electronics and Microelectronics
Engineering
Hilbert space
Instrumentation
Number theory
Preserves
Signal processing
Signal,Image and Speech Processing
Transformations
Transforms
Scrambling
Number theoretic transforms
Data security
Hilbert transforms
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Summary:This paper presents a general expression for a number theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform matrix together with alternating values in each row being zero and non-zero. Specific examples for 4-, 6-, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cryptographically useful scrambling transformations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-014-9759-8