Spectral width, frequency domain

The spectral width SWj relates to the frequency domain. With the variation of the evolution period tj, the intensity and phase of the signals... 

The spectral width SWi associated with the F, frequency domain may be dehned as F, = SWi. The time increment for the ti domain, which is the effective dwell time, DWi for this period, is related to SW as follows DWi = (V2)SW]. The time increments during [Pg.158]

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

Alternatively, the transmitter could be located in the centre of the spectrum. The choice was made, however, to record the spectrum with the F1 spectral width set to 350 ppm to intentionally spread out the correlations in the Fi frequency domain to avoid potential response overlaps. 

The laser used to generate the pump and probe pulses must have appropriate characteristics in both the time and the frequency domains as well as suitable pulse power and repetition rates. The time and frequency domains are related through the Fourier transform relationship that hmits the shortness of the laser pulse time duration and the spectral resolution in reciprocal centimeters. The limitation has its basis in the Heisenberg uncertainty principle. The shorter pulse that has better time resolution has a broader band of wavelengths associated with it, and therefore a poorer spectral resolution. For a 1-ps, sech -shaped pulse, the minimum spectral width is 10.5 cm. The pulse width cannot be <10 ps for a spectral resolution of 1 cm . An optimal choice of time duration and spectral bandwidth are 3.2 ps and 3.5 cm. The pump pulse typically is in the UV region. The probe pulse may also be in the UV region if the signal/noise enhancements of resonance Raman... 

A proof of this relation may be found in Bracewell (1978). Note that the spectral variable used in this and the next chapter is the same as that defined in Eqs. (7) and (8). Now consider a spatial distribution /(x) and its Fourier spectrum F(w) that come close to satisfying the equality in Eq. (4). We may take Ax and Aw as measures of the width, and hence the resolution, of the respective functions. To see how this relates to more realistic data, such as infrared spectral lines, consider shifting the peak function /(x) by various amounts and then superimposing all these shifted functions. This will give a reasonable approximation to a set of infrared lines. To discuss quantitatively what is occurring in the frequency domain, note that the Fourier spectrum of each shifted function by the shift theorem is given simply by the spectrum of the unshifted function multiplied by a constant phase factor. The superimposed spectrum would then be... 

Fig. 16.3. Schematic illustration of the interrelation between the temporal width of the laser pulse and the spectral width in the frequency domain.

NOESY was performed at 32 °C on a VXR-500 spectrometer operating at a proton frequency of 500 MHz. The protein was dissolved in 20 mM sodium phosphate, pH 7.5 (direct pH meter reading), 100 mM NaCl, 5 mM DTT in D2O. The protein concentration was 2 mM. The data was acquired in the hypercomplex mode with a mixing time of 150 ms (Jeener et al., 1979 Macura Ernst,1980). The spectral width was 7200 Hz in both dimensions. 2048 complex points in the t2 dimension and 256 complex points in the tl dimension were acquired. 96 transients were collected for each FID. Data processing was performed on a Sun Sparc 10 station using VNMR software from Varian. The time domain data were zero-filled once and multiplied by shifted sinebell or Gaussian functions before Fourier transformation in both dimensions. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d4. 

Alkali metal NMR spectra were observed at the appropriate resonance frequencies listed in Table I, using 12-mm tubes and a Varian XL-100 spectrometer with Gyrocode Observe capability. External 19F or internal H field-frequency lock was used. Depending on the linewidth of the resonance being observed, spectral widths of 256 Hz to 12 kHz in 8192 frequency domain points were used. For 23Na and 85Rb, 90° pulses of 50/isec and a 0.1-sec repetition rate were used. For 6Li and 133Cs, the approximately 55° pulses were 30 /xsec, and the pulse repetition rates for the Nafion samples were 60 sec and 1 sec, respectively. 

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