Digital resolution calculation

Liquid crystal display systems have been increasingly used in electro-optical devices such as digital watches, calculators, televisions, instmment panels, and displays of various kinds of electronic equipment, ie, lap-top computers and word processors. The dominant reason for thek success is thek extremely low power consumption. Furthermore, the Hquid crystal display systems have been remarkably improved in recent years, and today they have high resolution (more than 300,000 pixels) and full color capabiUty almost equivalent to those of a cathode ray tube. 

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

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 ... 

Digital resolution in the vj domain is a function of the number of data points (np2> and the spectral width (SW2) and is calculated in the same manner as for ID experiments (i.e., the acquisition of 2N data points results in N real points, after Fourier transformation) that describe spectra in the V2 dimension (Section 2-5d). If SW2 = 2,100 Hz and np2 = 1,024, then, after the FT, DR2 = sw2/(np2/2) = 2,100 Hz/(1,024/2) = 4.1Hz/point. Again as with ID experiments, one level of zero filling should be performed for optimum DR. If this is done, then np2 = 2,048. Using the real points obtained after the FT operation results in DR2 = 2,100Hz/(2,048/2) = 2.1 Hz/point. 

Figure 6.25. The HMBC long-range correlation spectrum of 6.2 recorded with A = 60 ms and with gradient selection. The sequence used the low-pass J-filter (Section 6.4.1) to attenuate breakthrough from one-bond correlations (which appear with Jch doublet structure along fj (arrowed)). IK ta data points were collected for 256 ti increments of 8 transients each and the data processed with unshifted sine-bells in both dimensions, followed by magnitude calculation. After zero-filling once in ti the digital resolution was 4 and 80 Hz/pt in f2 and fi respectively.

In examining the above figures, one can spot the discrete increments both in conversion (calculated from real-time conductivity readings) and in temperature. Part of the visible scatter is due to the limited 12-bit digital resolution of the data acquisition system used. A more sophisticated data logging board will reduce this form of scatter. 

Flat panel displays are a necessary prerequisite for the full visual availability of information. After development of passive matrix displays used in digital watches, calculators [160] and portable computers, intensive work started in the development of large-area, full colour active matrix liquid crystal displays with high resolution. At the present time, LCDs are a major market force rivaling cathode ray tubes [157a],... 

Fig. 16 The idea of a cube SMFT. (a) Scheme of a full 3D spectrum, containing peaks revealing E.COSY multiplet structure. The digital resolution is too low to approximate properly the narrow components of multiplets. (b) Scheme of a set of cubes , calculated just in vicinities of peaks, featuring much higher digital resolution. Determination of small coupling constants is possible. Reprinted with permission from [80]...

Figure 2-11. A plot of the stress measured during the three-point bending test for aged gels. The X indicates the point of fracture and used to calculate the modulus-of-rupture. The straight lines are set by the initial slope of the flexure cure and are used to obtain the elastic modulus. The area under the curve is the energy-to-break. The stair-stepfeatures in the data are due limited digitization resolution.

In recording the FID, the pulse width and read pulse (90°) must be set properly to assure highest possible sensitivity. Then the pulse delay time must be determined. It is normally set at 5x the longest T. Next the spectral width (SW) is set. In C NMR, the chemical shift range is 250 ppm, so at 50 MHz, the resonances will lie within 12,500 Hz which is the required SW. The number of data points (DP) must be 2" (from the FT algorithm) For NMR, 16K or 32K are usually considered sufficiently high. The digital resolution (DR) is calculated ... 

ELECTRODEjcls Fig. 4.24 The operation of an ion-specific electrode with a slope of 59.16 mV per decade for mono-valent ions (29.58 mV/dec for di-valent ions) is simulated under the assumption that a digital volt meter with a resolution of, say, 0.1 mV is used. The sample volume and the concentration of the metered titration solution are known. Normally, one would add a few milliliters of the concentrated titration solution and do the calculation spelled out in lines 140-150 in Table 4.22 here, because the sample concentration is known, the result can be normalized to it. The operation of short-cuts (volume correction), unknowns (volume bias, deviation of true slope from theoretical), and equipment shortcomings (digitization) can be studied. 

AAEP values calculated using eqn. (43) were observed to be within 0.13 mV of values obtained by digital simulation under conditions where the resolution of the simulation was 0.2 mV per time step for ip ranging from about 103 down to 0.75. In any event, eqn. (43) appears to describe AAEP to an accuracy well within experimental error. Some of the data are shown in Table 13. 

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