1,852 research outputs found
Compressed Sensing with Coherent and Redundant Dictionaries
This article presents novel results concerning the recovery of signals from
undersampled data in the common situation where such signals are not sparse in
an orthonormal basis or incoherent dictionary, but in a truly redundant
dictionary. This work thus bridges a gap in the literature and shows not only
that compressed sensing is viable in this context, but also that accurate
recovery is possible via an L1-analysis optimization problem. We introduce a
condition on the measurement/sensing matrix, which is a natural generalization
of the now well-known restricted isometry property, and which guarantees
accurate recovery of signals that are nearly sparse in (possibly) highly
overcomplete and coherent dictionaries. This condition imposes no incoherence
restriction on the dictionary and our results may be the first of this kind. We
discuss practical examples and the implications of our results on those
applications, and complement our study by demonstrating the potential of
L1-analysis for such problems
The detection of gear noise computed by integrating the Fourier and Wavelet methods
This paper presents a new gearbox noise detection algorithm based on analyzing specific points
of vibration signals using the Wavelet Transform. The proposed algorithm is compared with a previouslydeveloped
algorithm associated with the Fourier decomposition using Hanning windowing. Simulation
carried on real data demonstrate that the WT algorithm achieves a comparable accuracy while having a lower
computational cost. This makes the WT algorithm an appropriate candidate for fast processing of noise gear box
Discrete multitone modulation with principal component filter banks
Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel
WAVELET ANALYSIS CONSIDERATIONS FOR EXPERIMENTAL NONSTATIONARY FLOW PHENOMENA
In this work, wavelet transforms are the analysis tools for studying transient and discontinuous phenomena associated to turbulent flows. The application in quest results from velocity measurements with hot wire anemometry in the transient wake considering a circular cylinder in an aerodynamic channel. Continuous and discrete wavelet transforms are applied and compared with the corresponding results given by the Fourier transform. For the continuous wavelet transform, the Morlet function was adopted as transform basis, and for the discrete case, the Daubechies orthonormal wavelet with 20 null moments. Results using the discrete wavelet packet transform are also presented and compared. A wake past a cylinder was analytically simulated and compared with the actual one, both in transient flow. The ability of the wavelet transforms in the analysis of unsteady phenomena and the potential of the wavelet approach as a complementary tool to the Fourier spectrum for the analysis of stationary phenomena is presented and discussed
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