Computing linear transforms of symbolic signals

Signals that represent information may be classified into two forms: numeric and symbolic. Symbolic signals are discrete-time sequences that at, any particular index, have a value that is a member of a finite set of symbols. Set membership defines the only mathematical structure that symbolic sequen...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2002-03, Vol.50 (3), p.628-634
Main Authors: Wei Wang, Johnson, D.H.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Deoxyribonucleic acid
Discrete transforms
Exact sciences and technology
Information, signal and communications theory
Mathematical analysis
Mathematical methods
Mathematical models
Process design
Sequences
Signal analysis
Signal and communications theory
Signal design
Signal processing
Signal processing algorithms
Signal representation. Spectral analysis
Signal, noise
Spectra
Telecommunications and information theory
Time frequency analysis
Transforms
Wavelet analysis
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Description
Summary:Signals that represent information may be classified into two forms: numeric and symbolic. Symbolic signals are discrete-time sequences that at, any particular index, have a value that is a member of a finite set of symbols. Set membership defines the only mathematical structure that symbolic sequences satisfy. Consequently, symbolic signals cannot be directly processed with existing signal processing algorithms designed for signals having values that are elements of a field (numeric signals) or a group. Generalizing an approach due to Stoffer (see Biometrika, vol.85, p.201-213, 1998), we extend time-frequency and time-scale analysis techniques to symbolic signals and describe a general linear approach to developing processing algorithms for symbolic signals. We illustrate our techniques by considering spectral and wavelet analyses of DNA sequences.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.984752