Sampling the FID

The total sampling period of the FID, known as the acquisition time, is ultimately dictated by the frequency resolution required in the final spectrum. From the Heisenberg s Uncertainty Principle, the resolution of two lines separated by Ai/ Hz requires data collection for at least 1/Ai/ s. If one samples the FID for a time that is too short, then the frequency differences cannot be resolved and fine stmcture is lost (the minimum linewidth that can be resolved is given approximately by 0.6/AQ). Likewise, if the signal decays rapidly then one is unable to sample it for a long period of time and again can resolve no fine stmcture. In 

The acquisition time is defined by the digitisation rate, which is dictated by the spectral width and defines the sampling dwell time DW, and on how many data points are sampled in total. If the FID contains TD time-domain data points then  

Following the FT, two data sets are generated representing the real and imaginary spectra (Section 2.3), so the real part with which one usually deals contains half the data points of the original FID (in the absence of further manipulation), and its data size, SI, is therefore TD/2. DR is then  

digital resolution is simply the reciprocal of the acquisition time, so to collect a well-digitised spectrum one must sample the data for a long period of time clearly this is 

Whilst the NMR response decays throughout the FID, the noise component remains essentially constant and will eventually dominate the tail of the FID. At this point, there is little advantage in continuing acquisition since this only adds noise to the final spectrum. Provided the FID has fallen to zero when acquisition stops, one can artificially improve the digital resolution by appending zeros to the end of the FID. This process is known as zerofilling, and it interpolates these added data points in the frequency domain and so enhances the definition of resonance lineshapes (Fig. 3.15). 

Signals with frequencies less than or equal to the spectral width will be characterised correctly as they will be sampled at two or more points per wavelength, whereas those with higher frequencies will be incorrectly determined and in fact will appear in the spectrum at frequencies which are lower than their true values. To understand why this occurs, consider the 

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In practice we sample the FID for a duration of about 2-3 seconds till most of it has been recorded. This means that a small portion of the tail" of the FID will not be recorded. What effect would you expect this to have on the quality of the spectrum ... 

Figure 10.5 shows the FID obtained on a soap sample. The initial points of the FID yield information on the absolute proton signal intensity which is related to the total proton content in the sample. After the initial few points of the FID however, one must be careful with how the data are viewed quantitatively. Protons in different physical environments will have very different relaxation times. In the FID the differences in transverse (T2) relaxation are observed readily. In the case of the soap sample the FID contains a rapidly decaying signal at the beginning of the FID along with a signal that decays at a much slower rate. 

The free induction decay following 90° pulse has a line shape which generally follows the Weibull functions (Eq. (22)). In the homogeneous sample the FID is described by a single Weibull function, usually exponential (Lorentzian) (p = 1) or Gaussian (p = 2). The FID of heterogeneous systems, such as highly viscous and crosslinked polydimethylsiloxanes (PDMS) 84), hardened unsaturated polyesters 8S), and compatible crosslinked epoxy-rubber systems 52) are actually a sum of three... 

As a biologically relevant example of solid-state NMR on quadrupolar nuclei. Fig, 11 shows experimental and simulated Zn solid-state NMR spectra of zinc diimidazole diacetate which may be considered a model compound for Zn in metalloproteins. The experimental spectrum was obtained by sampling the FID in between the refocusing pulses in a quadrupolar version of the Carr-Purcell-Meiboom-Gill experiment (QCPMG), 5 In this manner, the hundred kHz wide second-order quadrupolar powder pattern is split into a manifold of spin-echo sidebands with the consequence of highly... 

Quantitation of the methane was obtained by comparing the detector response of a methane gas standard with that of the sample. The FID response was found to be linear with concentration throughout the entire range of methane concentrations encountered in the study. Standard gasses prepared by Matheson Gas Products were intercalibrated with a standard gas analyzed by the National Bureau of Standards (NBS). Analytical precision was generally less than 1% while accuracy, based on the NBS intercalibration, was 5%. The detection limit of the method, based on a signal-to-noise ratio of 2 is approximately 5 nL CH L- seawater (STP). 

The phase properties of MQC transfer echoes have also been employed to selectively detect desired orders of MQ spectra. Using the basic sequence (Fig. 2), an additional (fixed) period d is inserted in the MQ pulse sequence, prior to the mixing pulse of the MQ pulse sequence (Fig. 10). MQC evolves beyond the normal tx period and coherence transfer echoes of the TV-quantum coherences maximise in the detection period at a time TVJ.35,41,42 The echoes of different coherence orders maximise at different times in the detection period and the spectra of different orders of coherence can be obtained by sampling the FID in the appropriate window in the detection period. 

In general, the NMR spectrum of the object shows more than one resonance line, or in solids the lineshape is non-Lorentzian. Thus, the first exponential in Equation (5.6) needs to be replaced by the FID f t) in a homogeneous magnetic field. If the spectrum changes within the sample, the FID has to be placed inside the integral. 

Given that the ADC is only going to sample the signal at regular intervals the question arises as to how frequently it is necessary to sample the FID i.e. what should the time interval between the data points be. Clearly, if the time interval is too long we will miss crucial features of the waveform and so the digitized points will be a poor representation of the signal. This is illustrated in Fig. 5.7. 

The sampling theorem states that to record a spectrum unambiguously with frequencies as high as v, one must sample the FID at a rate of at least 2v (Nyquist frequency). For example, a 5 kHz wide 13C spectrum must be digitized at... 

The development has been slower in ESR as faster relaxation rates (three orders of magnitude) and wider spectral ranges (three-four orders of magnitude) have provided technical obstacles. The free induction decay (FID) can be employed to obtain spectra of paramagnetic species in liquids, analogous to the procedure in NMR. For solid samples the FID is usually too fast to obtain a spectrum. The electron spin echo modulation (ESEEM) method is the common technique to obtain spectra of paramagnetic species in solids. 

With very fast computer control, the complex FID can be sampled and the transform calculated in real time for several reasons using the trick of sampling the FID at time delays that correspond to a phase shift to obtain the sin(tot) sample as sin((i)f) = cos (tor + ir/2). Another featore of the pulse acquisition is that it is repeated many times to average the results. Thus we have a sitoation where a computer controls the timing of RF pulses perpendicular to the z-axis of the main magnet and many programs are available to carry out a nmnber of experiments with the same spectrometer. As such modem NMR spectrometers are programmable experiments. ... 

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