Complex data point

NMR Spectroscopy. All proton-decoupled carbon-13 spectra were obtained on a General Electric GN-500 spectrometer. The vinylldene chloride isobutylene sample was run at 24 degrees centigrade. A 45 degree (3.4us) pulse was used with a Inter-pulse delay of 1.5s (prepulse delay + acquisition time). Over 2400 scans were acquired with 16k complex data points and a sweep width of +/- 5000Hz. Measured spin-lattice relaxation times (Tl) were approximately 4s for the non-protonated carbons, 3s for the methyl groups, and 0.3s for the methylene carbons. 

The PVA sample was run at 55 degrees centigrade. A 90 degree (6.8us) pulse was used with a inter-pulse delay of 2.1s. Exactly 800 scans were acquired with 16k complex data points and a sweep width of +/-2000 Hz. 

With 2D experiments the situation is a little more complicated as the size of the overall digitised matrix depends on the number of time increments in tl as well as parameters specific to the 2D acquisition mode. Nevertheless, a digitised matrix of TD(2) X TD(1) complex data points is acquired and stored. Similar to ID the effective number o measured data points used for calculation TD(used) and the total number of data points SI to be transformed in t2 and tl may be defined prior to Fourier transformation. These parameters may be inspected and defined in the General parameter setup dialog box accessible via the Process pull-down menu. With 2D WIN-NMR the definitions for TD(2) and TD(1) are the same as for TD with ID WIN-NMR. However, unlike ID WIN-NMR, with 2D WIN-NMR SI(2) and SI(1) define the number of pairs of complex data points, instead of the sum of the number of real and imaginary data points. Therefore the 2D FT command (see below) transforms the acquired data of the current data set into a spectrum consisting of SI data points in both the real and the imaginary part. 

Another option is to use a multiwave technique, whereby the fundamental frequency and several other frequencies (harmonics) are added together into a single complex wave. Each one of these multiwave iterations can be deconvoluted into its components after the test is complete. Thus, each complex data point can... 

For the continuous-flow measurements, the pseudo-2D spectrum was recorded with a spectral width of 9616 Hz and 64 transients with 8K complex data points, thus resulting in an acquisition time of 0.42 s/transient along the 128 t increments. A relaxation delay of 1.2 s was used and the time resolution... 

Figure 8.2.15 One-dimensional spectra acquired with the four-coil probe. Each sample (250 mM in D2O) was loaded into the coil via the attached Teflon tubes 32 scans were acquired for each spectrum, with no delay between excitations of successive coils. Concurrent with the switch position being incremented, the spectral width was optimized for each compound 1 Hz line-broadening was applied before Fourier transformation and baseline correction. The spectral widths were (a) 600 Hz (galactose) (b) 1400 Hz (adenosine triphosphate) (c) 2000 Hz (chloroquine) (d) 500 Hz (fructose). 2048 complex data points were acquired for each spectrum, giving data acquisition times of approximately 1.7, 0.7, 0.5 and 2.0 s, respectively. The delay between successive 90 degree excitations was 4.9 s for each sample. Reprinted with permission From Li, Y., Walters, A., Malaway, P., Sweedler, J. V. and Webb, A. G., Anal. Chem.,l, 4815-4820 (1999). Copyright (1999) American Chemical Society...

Measured as dilute solutions (1.5 0.4% w/w) of an equimolar mixture of the secondary references and TMS in the solvents indicated, acquisition time 4 s, spectral width 4 kHz, 32 K complex data points. 6Hexamethyldisilane, (Me3Si)2 we prefer this abbreviation as it eliminates possible ambiguity (HMDS sometimes used for this reference is also used to denote HMDSO). 

The actual Fourier transform is a digital calculation, so not all frequencies are tested. In fact, the number of frequencies tested is exactly equal to the number of time values sampled in the FID. If we start with 16,384 complex data points in our FID (16,384 real data points and 16,384 imaginary data points), we will end up with 16,384 data points in the real spectrum (the imaginary spectrum is discarded). Another difference from the above description is that the actual Fourier transform algorithm used by computers is much more efficient than the tedious process of multiplying test functions, one by one, and calculating the area under the curve of the product function. This fast Fourier transform (FFT) algorithm makes the whole process vastly more efficient and in fact makes Fourier transform NMR possible. 

The spectra were acquired with 2048 t2 complex data points and 256 ri increments in the phase sensitive mode with quadrature detection using the method described by States et al. (25). Water resonance was supressed during the 1.5s relaxation period used in the NOESY, DQF-COSY and TOCSY experiments and the mixing period of the NOESY experiments by irradiating continuously at its resonance frequency. The amide exchange experiments were carried out by... 

Fig. 9 HNCO spectra of ubiquitin. Top panels show the addition of 0°, 90°, and 30° projections of the two jointly sampled indirect dimensions at a proton chemical shift of 8.14 ppm, reconstructed using back projection reconstruction. Each projection contains 52 complex points thus the total number of complex points sampled from left to right is 52, 104, and 156. The lower panel shows MaxEnt reconstruction using the same number of complex data points, distributed randomly along the nitrogen dimension (constant time) and with an exponentially decreasing sampling density decay rate corresponding to 15 Hz in the carbon dimension. A ID trace at the position of the weakest peak present in the spectrum is shown at the top of each spectrum (indicated by a dashed line). The insets depict the sampling scheme...

Figure 2 shows FM reconstructions using the five NUS schedules discussed above and compares the spectra with the reference (top). The bottom spectrum is a simulation of traditionally US acquired data for a 1,024 complex data point FID, processed with cosine apodization, one set of zero filling and Fourier... 

Complex data point. A data point consisting of both a real and an imaginary component. The real and imaginary components allowan NMR data set to be phase sensitive, insofar as there can occur a partitioning of the data depicted between the two components. An array of complex data points therefore consists of two arrays of ordinates as a function of the abscissa. 

Figure 7.1 Solution-state H NMR spectrum 3.33 ms per complex data point) and (simulated) of l-chloroethene for So = 2.3488 X 212 complex data points. At this resolution, v F = (1-5 X 10" ) X 100 MHz, T2 = 1 s, 11 distinct peaks are observed, spectral width = 300 Hz (digitization rate =...

Fig. 7.6 The first 1000 ms of the FID corresponding to the spectrum shown in Fig. 7.1. The digitization interval is 3.33 ms per complex data point, yielding a spectral width of 300 Hz, an unusually small spectral window. At 9.4 X H NMR is usuaiiy done with a 10 kHz spectral window, Cwith 25—50 kHz, and solid-state H with 1 MHz (and a corresponding 1 ps digiti-...

A virtual array transform using a window that can accommodate 2 complex data points can perform an N-point transform (N = 2 ) in the following four steps ... 

Figure 5. Top, normal proton spectrum of raffinose (0-a-D-galacto-pyranosyl -(l- 6) -a-D-gl ucopyranosyl-(l- 2)-D-fructofuranoside) in D2O) middle, tilted 2D J spectrum dispTayed as a series of traces across f2 bottom, integral projection of the absolute value of the tilted 2D spectrum onto the f2 axis, showing partially suppressed multiplet structure. All spectra were obtained on an XL-200 spectrometer, using continuous saturation to suppress the HDD solvent signal. The 2D spectrum employed 256 x 64 complex data points.

Figure 26 Schematic illustrations of correlation between the phases of rf pulses and of the individual complex data points of NMR spectra. Reproduced from Ref. [95] with permission of the PCCP Owner Societies.

Figure 5 The 500 MHz DQF-COSY spectrum of a shortened analogue of insulin, des-(B26-B30)-pentapeptide insulin in D2O. The spectrum was recorded on a Bruker AM 500 spectrometer interfaced with an ASPECT 3000 computer in a phase-sensitive mode. 2048 complex data points were acquired in the fs dimension, with a total of 512 free induction decays (FID) collected for transformation in the dimension. Each FID was acquired with a total of 128 scans.

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