Digitizer resolution

Resolution is an important consideration in any experiment involving a number of closely spaced maxima. The digital resolution (DR) achievable in an nmr spectmm is defined by the relation... 

For impurity signals in high-quality chemicals, the digital resolution of the instrument may encroach on the repeatability figure-of-merit,... 

The digital resolution of equipment and the limited numerical accuracy of calculators/programs,... 

Figure 2.4. Graph of the linear regression line and data points (left), and the residuals (right). The fifty-fold magnification of the right panel is indicated the digital resolution 1 mAU of a typical UV-spectrophotometer is illustrated by the steps.

Kaye, W. and Barber, D., Noise and Digital Resolution in a Microprocessor-Controlled Spectrophotometer, Ano/. Chem. 53, 1981, 366-369. 

Apparently, the digital resolution (DR) depends on the amount of computer memory used in recording the spectrum. If the memory size is M, then there will be M/2 real and M/2 imaginary data points in the frequency spectrum, and the separation (in hertz) between these data points (DR) will be given by ... 

We should decide in advance the digital resolution at which we wish to acquire a spectrum and then set the acquisition time accordingly. The acquisition time AT (that is, the product of the number of data points to be collected and the dwell time between the data points) is calculated as simply the reciprocal of the digital resolution ... 

A poor digital resolution will result in loss of some of the fine structure of an NMR signal. To increase the digital resolution, we need either to maintain the same number of data points but reduce the spectral width or, alternatively, to maintain the spectral width but increase the number of data points. Which method would you prefer for achieving a better signal-to-noise ratio ... 

Figure 1.29 shows the effect of digital resolution on the appearance of signals. It is important to remember that each data point in the FID contains information about every peak in the spectrum, so as more data p>oints are accumulated, and the FIDs acquired for a longer period, a finer digital resolution is achieved. 

Figure 1.29 The effect of increased digital resolution (DR) on the appearance of the NMR spectrum, (a) The spectrum of odichlorobenzene recorded at a digital resolution of 0.1 Hz per point, allowing the sj>ectral lines to be seen at their natural line width, (b) The spectrum of the same molecule recorded at a digital resolution of 0.4 Hz per point.

It is better to maintain the same number of data points and reduce the spectral width as far as possible. In the alternative case, the improved digital resolution will be at the cost of sensitivity, since it will produce a corresponding increase in acquisition time, AT. Either a greater time period would then be required or a lesser number of scans would be accumulated in the same time period, with a corresponding deterioration in the signal-to-noise ratio. 

The effective resolution is determined by the number of data points in each domain, which in turn determines the length of t and <2- Thus, though digital resolution can be improved by zero-filling (Bartholdi and Ernst, 1973), the basic resolution, which determines the separation of close-lying multiplets and line widths of individual signals, vdll not be altered by zero-filling. 

The number of data points to be chosen in the Fj and F2 domains is dictated not only by the desired resolution but by other, external considerations, such as the available storage space in the computer, and the time that can be allocated for data acquisition, transformation, and other instrument operations. Clearly, to avoid any unnecessary waste of time, we should choose the minimum resolution that would yield the desired information. Thus, if the peaks are separated by at least 1 Hz, then the desired digital resolution should be R/2 = V2 Hz to allow for signal separation in the F domain. The resolution considerations in the F and F domains may be different, depending on what information is required from each domain... 

In the case of the t domain, since it is only the number N of data points that determines the resolution, and not the time involved in the pulse sequence with various delays, it is advisable to acquire only half the theoretical number of FIDs and to obtain the required digital resolution by zero-filling. Thus the resolution in the Fi domain will be given by R = 2SWi/A i that in the F2 domain is given by / = 1/AQ = 2SW2/A2. 

TDj, ti time domain data points TD, time domain pairs of data points SI2 and SIi, total data points in Fj and F, domains, respectively Hz/PTj and Hz/PT], digital resolution in F and F, (real) domains NS, number of acquired transients DS, number of dummy transients Tr, recycle time. 

Figure 5.28 A schematic drawing of an AMX spin system representing coupling interactions recorded at low digital resolution so that no fine splittings are visible. Note the symmetrical appearance of the cross-peaks on either side of the diagonal.

Figure 5.29 (a) The H-NMR spectrum of ethyl acrylate showing signals for olefinic protons, (b) A phase-sensitive COSYsjiectrum recorded at higher digital resolution, (c) Expansion of the downfield cross-peak identified by a dashed circle in (b). 

It is easier to obtain a higher digital resolution in 2D experiments in the domain than in the domain, since doubling the acquisition time <2 results in little overall increase in the experiment time. This is so because... 

Digital resolution The distance, in hertz, between successive data points determines the extent of peak definition by the data points. 

Zero-filling A procedure used to improve the digital resolution of the transformed spectrum (e.g., in the tj domain of a 2D spectrum) by adding zeros to the FID so that the size of the data set is adjusted to a power of 2. Zero-quantum coherence The coherence between states with the same quantum number. It is not observable directly. 

Referring to phase encoding gradient pulses according to Figure 2.9.4(b), the digital resolution and the velocity field of view are given by [28]... 

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