Symbolic signal processing

Signals that represent information may be classified into two forms: numeric and symbolic. Symbolic signals are discrete-time sequences which have a value at any particular index that is a member of a 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 or group (numeric signals). 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 apply our techniques to the spectral and wavelet analysis of DNA sequences.