Line-broadening function

Fig. 5a-e FID of compound 1. a Original data b multiplied by a negative line broadening function (-0.3 Hz) c multiplied by a shaped sine bell function (SSB = 1) d multiplied by a positive line broadening function (0.8 Hz) e multiplied by a positive line broadening function (1.9 Hz)... 

EM affects the linewidth and is often also known as a line broadening function LB. A positive value of LB (here 0.8 and 1.9 Hz) broadens the lines, a negative value (here -0.3 Hz) sharpens them however, never forget that we are only modifying the information present, so that a decrease in the line-width is automatically accompanied by an increase in the baseline noise. This becomes clear immediately when we see the spectra of the OCH2 multiplet shown in Fig. 6. 

Fig. 8. The 195Pt-NMR spectra of a DMF solution of [Pt2(en)3(PRI)2(N02) (N03)](N03)2 0.5 H20 (11) at 5°C, acquired on a Bruker WM-250 spectrometer operating at 53.6 MHz. (a) Power spectrum of the Fourier transform of a 1 K FID accumulated with a 5-jjls pulse width, 100-kHz spectral width, and 2000 K transients, (b and c) Normal Fourier transforms of 1 K FIDs accumulated with 10-fis pulsewidths, 42-kHz spectral width, and 64 K transients per spectrum. All FIDs were treated with 400-Hz line broadening functions to suppress noise (58).

The composite filter 7(g)) may either be the true inverse filter, truncated for oo large if necessary, or any of the variations described in Section IV. In their original work, Rendina and Larson chose 7(g)) = (co)/t(co), where //(co) is a Gaussian line-broadening function that limits the ultimate resolution obtainable but yields a manageable 7(g)). For their studies Rendina and Larson used Ns = 4. 

Thus Eqs. (17) and (22) establish the explicit correlation between the fluorescence Stokes shift function and the line-broadening function that gives linear absorption and emission spectra via... 

The H LC-NMR spectra were obtained on peaks stored in the BPSU-36 storage loops. Data were acquired with WET [41] solvent suppression on the residual water and acetonitrile signals. A composite 90° observe pulse, (tt/2)y—(tt/2) x—(tt/2) y—(tt/2)x, was employed. Spectra were collected into 32K data points over a width of 12 019 Hz, giving an acquisition time of 1.36 s, with an additional relaxation delay of 1.5 s. The data were multiplied by a line-broadening function of 1 Hz to improve the signal-to-noise ratio and zero-filled by a factor of two before Fourier transformation. 

Lorentzian line broadening function. The apodization function most commonly used to emphasize the signal-rich initial portion of a digitized FID. 

The type of the line-broadening function (LBF) may be either Lorentzian or Gaussian. The appropriate type depends on the nature of the line broadening mechanism. If in doubt it is recommended to start with a Lorentzian shape. After you have selected a file and wavenumber range as usual in the dialog box (Fig. 10.50), specify on the Adjust Parameter page a deconvolution factor and a suppression factor for the noise, or alternatively, a factor for the bandwidth and the resolution enhancement. Start the function using the Deconvolute button. 

The dephasing of the ensemble thus is contained in the relaxation function (p m t) = with gnm f) (sometimes called the lineshape or line-broadening function) defined in Eq. (10.66a). 

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