KEYWORDS: Fermium, Frequency modulation, Wavelets, Denoising, Wavelet transforms, Signal processing, Electronic filtering, Signal to noise ratio, Interference (communication), Process modeling
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.
Wavelet filter banks are potentially useful tools for analyzing and extracting information from frequency modulated (FM) signals in noise. Chief among the advantages of such filter banks is the tendency of wavelet transforms to concentrate signal energy while simultaneously dispersing noise energy over the time-frequency plane, thus raising the effective signal to noise ratio of filtered signals. Over the past decade, much effort has gone into devising new algorithms to extract the relevant information from transformed signals while identifying and discarding the transformed noise. Therefore, estimates of the ultimate performance bounds on such algorithms would serve as valuable benchmarks in the process of choosing optimal algorithms for given signal classes. Discussed here is the specific case of FM signals analyzed by Morlet wavelet filter banks. By making use of the stationary phase approximation of the Morlet transform, and assuming that the measured signals are well resolved digitally, the asymptotic form of the Fisher Information Matrix is derived. From this, Cramer-Rao bounds are analytically derived for simple cases.
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.
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