Proceedings PaperIdentification of noisy FM signals using nonorthogonal wavelet transforms
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An effective realization of a frequency modulation identification scheme requires an analysis tool which is capable of crisply extracting a signal's frequency fluctuations over time. Such an analysis should be digitally tractable, computationally efficient, concise, noise robust, and not too sensitive to time-shifts. In all these respects, non-orthogonal wavelet transforms (NOWTs) are well suited for the analysis of FM signals. Because no orthogonality is required of the wavelet family, the analyzing wavelet may be chosen almost arbitrarily. This freedom may be exploited to specify special families of wavelets which are defined directly in the frequency domain on a frequency interval of support described by a center frequency, and bandwidth. In general, these parameters may be used to tune the wavelet family to a particular class of signals of interest. A signal's frequency modulation may be estimated through simple coherent identification schemes in the NOWT domain, e.g., thresholding. Identification may then be subsequently performed via a simple nearest neighbor thresholded classifier using a specified metric (notion of distance). This approach is applied to a small test set of mono-component and multi-component synthetic FM signals and shown to yield 100% identification success at signal to noise ratios greater than -4dB using a Morlet based NOWT. For comparison, the same data set yields 100% identification success for signal to noise ratios only as low as 0dB when comparing signals directly in the time domain, i.e., via a matched filter technique.