DocumentCode
1191666
Title
The Smith-Barnwell condition and nonnegative scaling functions
Author
Janssen, A.J.E.M.
Author_Institution
Philips Res. Lab., Eindhoven, Netherlands
Volume
38
Issue
2
fYear
1992
fDate
3/1/1992 12:00:00 AM
Firstpage
884
Lastpage
886
Abstract
It is shown that any periodic function m/sub 0/( zeta ) with nonnegative Fourier coefficients that satisfies the Smith-Barnwell conditions m/sub 0/(0)=1, mod m/sub 0/( zeta )/sup 2/+ mod m/sub 0/( zeta + pi ) mod /sup 2/=1 is of the form m/sub 0/( zeta )=exp(il zeta /2) cos k zeta /2 with l, k odd integers. As a consequence it is concluded that any nonnegative scaling function with orthonormal integer translates is of the form x/sub (k,k+1)/ with k in Z.<>
Keywords
signal processing; transforms; Smith-Barnwell condition; multiresolution analysis; nonnegative scaling functions; orthonormal integer translates; periodic function; signal analysis; wavelets; Erbium; Multiresolution analysis; Ovens;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.119746
Filename
119746
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