Fourier-averaging technique

Each of the two noise-methods mentioned uses a periodic excitation by noise to produce a periodic response, apparently, so that signal-averaging techniques may be used to (a) diminish the total quantity of data stored, and (b) permit the computation of crosscorrelation and Fourier-transform functions as discrete sums of a reasonably finite number of terms.162,163... 

The problem of existence and stability of limit cycles has been attadred in many ways. Luus and Lapidus have used an averaging technique, Douglas et employ a perturbation analysis, and Gilles and Hyon and Aris use Fourier transform methods to examine the occurrence of limit cycles, all with moderate successes. More recently Uppal et a/. have discussed the dynamic behaviour of the CSTR in terms of the bifurcation of the steady state, devdoping critmia for the existence and stability of oscillatory states as a function of system parameters, and... 

FT NMR excite all nuclei of a given species simultaneously. Therefore, the FID is a complex interferogram consisting of the superposition of a number of damped oscillations with resonance frequency and relaxation time characteristic of each chemically distinct nuclear environment. Fourier transformation separates the components in the frequency domain. The same chemical shift information is obtained as in CW NMR but in a timescale of seconds rather than minutes. FT NMR is therefore a much more efficient method for the application of time-averaging techniques. 

Most modern NMR spectrometers use the Fourier transform technique, similar to that used in infrared spectroscopy. There is no need to scan the magnetic field, so spectra can be taken quickly. The spectrum can be obtained repeatedly and the individual spectra can be added, enhancing the signal and averaging out much of the noise. This is an advantage with which has a natural abundance of only 1% and therefore gives only a weak NMR signal. 

Most operations of the instrument are under computer control. The spectrum is recorded as a series of data points, along a linear axis of magnetic field. The signal-to-noise ratio can be improved by repetitive scanning and signal averaging. Fourier transform techniques are normally only used for analysis of pulsed EPR experiments. There is a range of different software for analysis of the spectroscopic data, in particular for simulation. 

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