The Smith-Barnwell condition and nonnegative scaling functions

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Abstract

It is shown that any periodic function m0(¿) with nonnegative Fourier coefficients that satisfies the Smith-Barnwell conditions m0(0) = 1, |m0(¿)|2 + |m0(¿ + p)|2 = 1 is of the form m0(¿) = exp(il¿/2) cos k¿/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[k, k+1) with k e Z.
Original languageEnglish
Pages (from-to)884-886
Number of pages3
JournalIEEE Transactions on Information Theory
Volume38
Issue number2
DOIs
Publication statusPublished - 1992

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