Wavelet Spectra compared to Fourier
نویسنده
چکیده
The relation between Fourier spectra and spectra obtained from wavelet analysis is established. Small scale asymptotic analysis shows that the wavelet spectrum is meaningful only when the analysing wavelet has enough vanishing moments. We relate these results to regularity theorems in Besov spaces. For the analysis of innnitly regular signals, a new wavelet, with innnit number of cancellations is proposed.
منابع مشابه
Isogeometric analysis: vibration analysis, Fourier and wavelet spectra
This paper presents the Fourier and wavelet characterization of vibratio...
متن کاملWavelet- and Fourier-transform-based spectrum similarity approaches to compound identification in gas chromatography/mass spectrometry.
The high-throughput gas chromatography/mass spectrometry (GC/MS) technology offers a powerful means of analyzing a large number of chemical and biological samples. One of the important analyses of GC/MS data is compound identification. In this work, novel spectral similarity measures based on the discrete wavelet and Fourier transforms were proposed. The proposed methods are composite similarit...
متن کاملA WAVELET-BASED PROCEDURE FOR MINING OF PULSE-LIKE GROUND MOTIONS FEATURES ON RESPONSE SPECTRA
The main objective of this paper is to present a wavelet-based procedure to characterize principle features of a special class of motions called pulse-like ground motions. Initially, continues wavelet transform (CWT) which has been known as a powerful technique both in earthquake engineering and seismology field is applied easily in automated detecting of strong pulse of earthquakes. In this pr...
متن کاملAssessment of the Wavelet Transform for Noise Reduction in Simulated PET Images
Introduction: An efficient method of tomographic imaging in nuclear medicine is positron emission tomography (PET). Compared to SPECT, PET has the advantages of higher levels of sensitivity, spatial resolution and more accurate quantification. However, high noise levels in the image limit its diagnostic utility. Noise removal in nuclear medicine is traditionally based on Fourier decomposition o...
متن کاملNoise reduction in astronomical spectra using wavelet packets
The wavelet representation of a signal offers greater flexibility in de-noising astronomical spectra than classical Fourier smoothing due to the additional wavelength resolution of the decomposed signal. We present here a new wavelet-based approach to noise reduction. It is similar to an application of the splitting algorithm of a wavelet packets analysis using non-orthogonal wavelets. It clear...
متن کامل