Short-time noise,

For the sake of illustration, a TOF analyzer could be likened to a camera taking snapshots of the m/z values of an assembly (beam) of ions the faster the repetition rate at which the camera shutter is clicked, the greater is the number of mass spectra that can be taken in a very short time. For TOF analyzers, it is not uncommon to measure several thousand mass spectra in one second All such spectra can be added to each other digitally, a process that improves the signal-to-noise ratio in the final accumulated total. 

Few (4 to 8) [26] spectrometer scans are taken, averaged and stored while the electrode potential is held at a reference potential and then at a working potential. In this way only a short time is passed between the transition from the reference to the working condition. The sequence is repeated many times in order to improve the signal-to-noise ratio. 

Phase-sensitive detection is not at all specihc for EPR spectroscopy but is used in many different types of experiments. Some readers may be familiar with the electrochemical technique of differential-pulse voltammetry. Here, the potential over the working and reference electrode, E, is varied slowly enough to be considered as essentially static on a short time scale. The disturbance is a pulse of small potential difference, AE, and the in-phase, in-frequency detection of the current affords a very low noise differential of the i-E characteristic of a redox couple. 

Figure 37. The maximum of the mean curvature distribution scaled with the interface density increases very rapidly (up 2.5 times) within a short time interval, x , after the noise term has been switched off in the simulation. The Euler characteristic and the average domain size, / o, remain constant, and the surfaces area decreases by 3%. This illustrates that the curvature distributions are very sensitive to the thermal undulations of the interface. The times are x = 0.0, 0.032, 0.085, 0.225, 0.896, 2.05 from bottom to top at /// ] 0.

Practicable isotopic enrichment has the following prerequisites adequately short time for the enrichment process, acceptable asymptotic enrichment factor, and adequate accuracy for the estimation of the enrichment factor. (When total activity, rather than specific activity, is limiting, one must also pay attention to losses during enrichment.) For the argon and carbon enrichments referred to above, enrichment factors of about 100 and 500 were obtained within a week and a few hours, respectively and enrichment factors were deduced from direct observations of adjacent, stable isotopes. The 14C enrichment process provided extra dividends for AMS measurement the sample was implanted in an ideal form for the accelerator ion source, and it was spatially localized (depth) which gave added signal-to-noise enhancement. 

The advantages of CC in ultra trace analysis are shown to be unmistakable. The quantitative reliability of the method was demonstrated by the extension of a calibration graph for phenol to two decades of concentration more when compared with conventional chromatography. A considerable improvement of the signal-to-noise ratio can be achieved in a relatively short time. The method offers excellent prospects for ultra trace analysis in cases where preconcentration of the solute fails. 

Al MAS NMR has been demonstrated to be an invaluable tool for the zeoHte sdentist It provides a simple and direct way to quantify the proportions of A1 in four [Al(4)j, five [Al(5)j and six [Al(6)j coordinations. Quantitative determination of these species is an important issue in catalysis, and major effort is devoted on this topic. As mentioned already, for A1 only the central transition (-i-half to —half selective exdtation ) is detected. The central transition is unaffected by first order quadmpolar interaction, but the presence of second order effects causes broadening and complicates the quantitation of the A1 species. Usually hydrated samples and short radiofrequency pulses are employed for quantitative determination of framework and extra framework aluminum species. It is uncertain whether hydration changes the coordination of A1 species. Certain extra framework A1 can have very large quadmpolar interactions resulting in very broad lines ( NMR invisible ) [155, 202]. Unlike Si NMR, Al has a short relaxation time due to its quadmpolar nature, and the Al NMR spectrum with good signal to noise can be obtained in a relatively short time. 

The Impedance Z can Increase to very high values. If this happens, the oscillator prefers to oscillate In resonance with an anharmonic frequency. Sometimes this condition Is met for only a short time and the oscillator oscillation jumps back and forth between a basic and an anharmonic oscillation or It remains as an anharmonic oscillation. This phenomenon Is well known as "mode hopping". In addition to the noise of the rate signal created, this may also lead to Incorrect termination of a coating because of the phase jump. It Is Important here that, nevertheless, the controller frequently continues to work under these conditions. Whether this has occurred can only be ascertained by noting that the coating thickness Is... 

Progress has been recently made in constructing an iterative inverse Laplace transform method which is not exponentially sensitive to noise. This Short Time Inverse Laplace Transform (STILT) method is based on rewriting the Bromwich inversion formula as ... 

Detector sensitivity is one of the most important properties of the detector. The problem is to distinguish between the actual component and artifact caused by the pressure fluctuation, bubble, compositional fluctuation, etc. If the peaks are fairly large, one has no problem in distinguishing them however, the smaller the peaks, the more important that the baseline be smooth, free of noise and drift. Baseline noise is the short time variation of the baseline from a straight line. Noise is normally measured "peak-to-peak" i.e., the distance from the top of one such small peak to the bottom of the next. Noise is the factor which limits detector sensitivity. In trace analysis, the operator must be able to distinguish between noise spikes and component peaks. For qualitative purposes, signal/noise ratio is limited by 3. For quantitative purposes, signal/noise ratio should be at least 10. This ensures correct quantification of the trace amounts with less than 2% variance. The baseline should deviate as little as possible from a horizontal line. It is usually measured for a specified time, e.g., 1/2 hour or one hour and called drift. Drift usually associated to the detector heat-up in the first hour after power-on. 

A phenomenon defined as fast changes in the intensity and frequency of a measured signal irrespective of the presence or absence of the analyte. The speed of change is significantly different from the normally expected detector response. A measure of noise is the measured difference between the highest and lowest value of the measured signal with no analyte present, observed in a relatively short time-span, as compared to the time-span necessary for measurement of the analyte. 

With the low concentration of tropospheric HO and the desire for measurements of fairly short time duration, all techniques have struggled with signal-to-noise ratio problems, and users of each method have gone to some lengths to improve this ratio. Additionally, interference problems, which... 

Ju. For T2 <3C 1/(27//), maximal intensity is obtained for fj = 27 ./ and tf = 2T(. Of course, at these short time values, the sine build up of the interaction is small. Weighting functions of sin, sin2 or matched-filter-type are used to maximize the signal-to-noise ratio. In any case, since the T2 values in paramagnetic compounds are small, the cross peak intensity is drastically reduced. 

Another model which is a strong candidate for musical signals is the sinusoidal model, which has been used effectively for speech applications ([McAulay and Quatieri, 1986b] and chapter 9 of this book). A constrained form of the sinusoidal model is implicitly at the heart of short-time spectral attenuation (STSA) methods of noise reduction (see section 4.5.1). The model is also a fundamental assumption of the pitch variation algorithms presented in section 4.6. In its general form the signal can be expressed as ... 

Background noise reduction by short-time spectral attenuation... 

For the STFT case, the bandwidth of the filter-bank is inversely proportional to the duration of the short-time frame and it is shown in [Cappe and Laroche, 1995], using standard results concerning the simultaneous frequency masking phenomenon, that the processing can suppress audible signal components (ie. components that were not masked by the additive noise) if the short-time duration is well below 40 ms. 

Improving the properties of the short-time transform. Another interesting area of research deals with the design of the short-time transform. It is striking to see that while many efforts have been dedicated to the study of advanced suppression rules, little has been done concerning the analysis part of the noise reduction-system. 

Several techniques have been proposed for modifying the shape of the short-time spectrum so as to emphasize those portions deemed to be important for speech perception or to reduce the amplitude of those portions assumed to be noise. One approach is adaptive comb filtering[Lim et al., 1978], In this method, the fundamental frequency of voiced speech sounds is estimated, and a comb fdter is then constructed to pass signal power in the regions of the pitch harmonics and to suppress power in the valleys in between. Experimental results with normal-hearing subjects, however, have shown no significant improvement in intelligibility with this type of system [Perlmutter et al., 1977][Lim et al., 1978],... 

Background noise suppression by short- time spectral attenuation 165... 

Certainly the most popular methods for noise reduction in audio signals to date are based upon short-time Fourier processing. These methods, which can be derived from non-stationary adaptations to the frequency-domain Wiener filter, are discussed fully in section 4.5.1. 

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