DocumentCode
1175117
Title
Matrix formulation of the discrete Hilbert transform
Author
Burris, Frank E.
Volume
22
Issue
10
fYear
1975
fDate
10/1/1975 12:00:00 AM
Firstpage
836
Lastpage
838
Abstract
The discrete Hilbert transform (DHT) of a periodic sequence is interpreted as a matrix product 
. A new singleequation form of the DHT operation for any number of sample points 
is shown and is used to establish the unique properties of the coefficient matrix 
. is shown to be highly symmetric in nature, and the determination of the elements of is shown to require a minimum of computation; i.e., less than elements need to be computed for an 
matrix. For the even case, the relatively sparse nature of is established; i.e., at least half the elements of are zeros.
. A new singleequation form of the DHT operation for any number of sample points is shown and is used to establish the unique properties of the coefficient matrix . is shown to be highly symmetric in nature, and the determination of the elements of is shown to require a minimum of computation; i.e., less than elements need to be computed for an matrix. For the even case, the relatively sparse nature of is established; i.e., at least half the elements of are zeros.Keywords
Discrete Hilbert transforms; Matrix methods; Circuit theory; Computer simulation; DH-HEMTs; Discrete Fourier transforms; Discrete transforms; Electrons; Equations; Symmetric matrices; Transfer functions; Voltage;
fLanguage
English
Journal_Title
Circuits and Systems, IEEE Transactions on
Publisher
ieee
ISSN
0098-4094
Type
jour
DOI
10.1109/TCS.1975.1083968
Filename
1083968
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