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Makhoul's conjecture for p = 2
- Source :
- ICASSP
- Publication Year :
- 2002
- Publisher :
- IEEE, 2002.
-
Abstract
- The IEEE Signal Processing Society (2000) offered a prize of $1000 for proving or disproving Makhoul's conjecture, which says that, given a causal all-pass digital signal x/sub n/ of order p, with nonzero x/sub 0/, the location of the peak of x/sub n/ always lies between n = 0 and n = 2p-1. The case of p = 1 is trivial, and no further progress had been made in 25 years until Lertniphonphun, Rajagopal, and Wenzel gave counter examples for large p. In this paper, Makhoul's conjecture is proven for p = 2. It is also shown that the conjecture fails dramatically in the case of complex coefficients.
Details
- Database :
- OpenAIRE
- Journal :
- 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
- Accession number :
- edsair.doi...........1d9441f9ea24143dcbde8775326e14b2