Signal processing decomposition

Liu XQ, Sidiropoulos ND, Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays, IEEE Transactions on Signal Processing, 2001,49, 2074—2086. 

S. Mallat, Multifrequency Channel Decompositions of Images and Wavelet Models, IEEE Transactions on Acoustics Speech and Signal Processing, 37 (1989), 2091-2110. 

Based (somewhat) on the frequency analysis properties of the human ear and auditory system, a common signal processing technique involves splitting sound into separate frequency bands. A common decomposition is based on octaves, successively dividing the spectrum by two. Ten bands are required... 

Signal processing for tool condition monitoring from wavelet analysis to sparse decomposition... 

Liu, B., Riemenschneider, S. Xu, Y. 2006. Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum. Mechanical Systems and Signal Processing 20 (3) pp. 718-734. 

Tsai, R.Y., Huang, T.S. and Zhu, W., "Estimating three-dimensional motion parameters of a rigid planar patch, II Singular value decomposition," IEEE Transaction on Acoustics, Speech, and Signal Processing, vol. ASSP-30, no.4, pp.525-534, Aug 1982. 

The primary process of SiH decomposition is electron impact which produces a large number of different neutral and ionic species as shown in Table 1. The density of S1H2 and SiH neutral species produced has been found to be much larger than the density of the ions. For example, mass spectrometric data for silane discharges indicate that the density of ionic species is lower by 10 compared with the density of neutral species. Further, mass spectrometer signals of ionic species, such as SiH SiH 25 SiH", SiH", and Si2H , increase by more than two orders of magnitude as the r-f power is increased, eg, from 2 to 20 W. A rapid rise in the population of ions, with power, implicitly means an increase in electron density. 

For real-world signals with finite records, the convolution processes leading to decomposition and reconstruction of a signal, require data in regions beyond the signal s endpoints. Assuming a mirror image of the... 

Fig. 14. Esxtracting distinguishing features from noise pulse signal. Wavelet coefficients in shaded regions represent stable extrema, (a) Wavelet decomposition of noisy pulse signal (b) wavelet decomposition of pulse signal. (Reprinted from Bakshi and Stephanopoulos, Representation of process trends. Part III. Computers and Chemical Engineering, 18(4), p. 267, Copyright (1994), with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.)...

Cu(II) EPR signal in nitriles as solvent as well as by polarographic measurements 144>. Similarly, the EPR signal disappeared when Cu(OTf)2 was used for catalytic cyclo-propanation of olefins with diazoesters 64). In these cases, no evidence for radical-chain reactions has been reported, however. The Cu(acac)2- or Cu(hfacac)2-eatalyzed decomposition of N2CHCOOEt, N2C(COOEt)2, MeCOC(N2)COOEt and N2CHCOCOOEt in the presence of cyclopropyl-substituted ethylenes did not furnish any products derived from a cyclopropylcarbinyl - butenyl rearrangement128. These results rule out the possible participation of electron-transfer processes and radical intermediates which would arise from interaction between the olefin and a radical species derived from the diazocarbonyl compound. 

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