A it transform--model based approach for suppressing noise in frequency modulated (FM) signals is presented. This approach is based on a model of the expected output of a wavelet filter bank in response to a noise-free FM signal. Resolving the discrepancy between filter bank output in response to a noisy FM signal and the expected output given by the model provides the mechanism for noise suppression. Specifically, a stationary phase approximation to the Morlet wavelet transform is used to form the model. The approach is shown to perform favorably on a numerical example when compared to both simple lowpass filtering (linear) and wavelet thresholding (non-linear) denoising techniques.
We present an approach to complex signal identification that uses a non-linear transformation into a 2-D (image) domain as a fundamental first step. Motivating this approach is the observation that many complex signals of interest have characteristic complex--plane behaviors when viewed under certain invariance rules, e.g., rotation and/or scaling in the complex--plane. Orthonormal bases in 2D that exhibit special properties may be employed to some advantage for 1D classification. Specifically, we use the Zernike transform to yield rotationally invariant features of complex 1D signals. These features may be furthered projected into a low dimensional subspace via a standard Fisher analysis in the context of a specific data set. Using a small data set consisting of six different sources the method is shown to perform well and exhibit a high level of noise robustness. The resulting feature vector is of low dimensionality and has reasonable computational cost.
We present a framework for the use of stationary phase approximations to a Morlet wavelet transform as a device to generate computationally efficient algorithms for extracting modulation information in frequency modulated (FM) signals. Presented here are two specific FM estimators generated from this approach that may be implemented in terms of filter banks with very few filters.
This paper addresses the issue of extracting fine-frequency modulation laws from narrow-band pulsed signals and provides a fast and efficient wavelet-based scheme for their extraction. Two distinct methods of frequency demodulation are analyzed: first, is standard direct extraction using the arctangent function and second, is estimation via wavelet transform ridges. The first method is predominant in applications because implementation is straightforward and computational complexity is small; however, such direct estimates have leading edge and trailing edge variability and are very sensitive to noise. The second wavelet-based method is shown to be robust to noise and provide crisp estimates of all modulation components in a signal. Both methods are numerically implemented in MATLAB and results are compared on a set of signals of interest. As compared to conventional direct estimation, this approach is shown to provide many benefits including noise robustness, estimate leading and trailing edge consistency, and pulse-to-pulse low variation.
KEYWORDS: Signal to noise ratio, Wavelet transforms, Chemical species, Wavelets, Frequency modulation, Signal processing, Fermium, Electronic filtering, Time-frequency analysis, Continuous wavelet transforms
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.
We present a highly powerful, modular, and interactive software tool for the analysis of time- frequency coherent signals via wavelet transformations. A major design goal of the Wavelet Signal Processing Workstation (WSPW) is to maximize ease of use while minimizing programming complexity. As such, the WSPW makes ample use of graphical mouse driven user interfaces and, in turn, allows powerful signal processing, classification, and identification techniques to be rapidly implemented and tested. Because it has been developed using MATLAB, the WSPW is easily extensible and inherently portable between varying system architectures. Although the emphasis of this paper is on the wavelet representation of signals, the WSPW has proven itself a valuable tool in applications including radar source identification and signal classification.
In this paper we introduce the concept of a local Hilbert space frame and develop theory for the representation and reconstruction of signals using local frames. The theory of global frames is due to Duffin and Schaeffer. Local frames are defined with respect to a global frame and a particular element from a Hilbert space H. For any signal f* (epsilon) H, H may be decomposed into two signal dependent subspaces: a finite dimensional one which essentially contains the signal f* and one to which the signal is essentially orthogonal. The frame elements associated with the former subspace constitute the local frame around f*.