Multidimensional signals

Tseng SY, Dustin ML (2002) T-cell activation a multidimensional signaling network. Curr. Opin. Cell Biol 14 575-580... 

Under the best of circumstances we can express the multidimensional signal (y) as a linear function of the unknown concentrations (xj ), such as decaying nuclear or optical spectra ... 

We now we summarize some of the procedures that are used in analyzing multidimensional IR data. Constants factors are often omitted from the formulas as are the transition dipole factors which are easily incorporated [74] when the modes are a collection of coupled harmonic oscillators. More generally the variations of transition dipole with nuclear displacement should be incorporated. It is often useful to compare the 2D-IR results with the results of other nonlinear experiments because it turns out that various manipulations of these multidimensional signals provide all of the common nonlinear results such as echoes, gratings, degenerate four wave effects, and pump-probe spectroscopy. 

LAURENT, G., Olfactory network dynamics and the coding of multidimensional signals. Nat. Rev. Neurosci., 2002, 3, 884-895. 

Mersereau RM, Oppenheim AV (1974) Digital reconstruction of multidimensional signals from their projections. Proc IEEE 62 1319-1338... 

The FT of the simplest multidimensional signal is thus a multidimensional delta function, i.e.. 

Again, signal frequency (frequencies) is (are) clearly visualized in the spectral domain as a peak centered at (vj, V2,..., v ). Its position informs about correlated frequencies present in the multidimensional signal, which is usually the most essential experimental information. 

Chellappa, R., Girod, B., Munson, D., Jr., Tekalp, M., and Vetterli, M. (1998). The Past, Present and Future of Image and Multidimensional Signal Processing. IEEE Signal Process. Mag. 15(2), 21-58. 

The problem is the reverse process, how to extract them and put in some logical sense, called models or theories. Modem digital technology has made it possible to manipulate multidimensional signals with systems that range from simple digital circuits to advanced parallel computers. When talking about sets of visual information, the process of their quantification for further analysis or observation can be set as follows ... 

An extension to two- resp. multidimensional filters is presented in Refs. 114, 167, 168. Matched filters are the most elegant solution, provided one knows what form the signal has. The choice between different filter types is discussed in Ref. 114. 

N. P. J. Price and R. W. Carlson, Rhizobial lipo-oligosaccharide nodulation factors multidimensional chromatographic analysis of. symbiotic signals involved in the development of legume root nodules, Glycobiology 5 233 (1995). 

Fig. 3.9. One-dimensional information (in y-direction) of a single signal at a fixed z-value (left-hand side) and quasi-multidimensional information on several analytes AyBy...,N as a sequence of one-dimensional information (right-hand side)... 

Multidimensional image information can be processed in the same way as signal functions in general. In many cases, the basis of image processing is the two-dimensional Fourier analysis... 

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