After data are acquired, the next step in the process is applying a “weighting function” to the FID, which is an optional part of the process, and Fourier transformation, which is not. Both operations are done using the Process page on the Process panel.

Linear Prediction in VnmrJ
In VnmrJ, linear prediction is incorporated directly into the Fourier transform routine, so that normally one does not see the “improved” FID, but merely the spectrum which results from Fourier transforming the linear predicted FID. This is accomplished by selecting the Linear Prediction check box in the Linear Prediction panel and clicking the Transform button. To see the linear predicted FID, it is possible to do so by entering ft('noft'), which performs all the steps of the Fourier transform routine except the actual Fourier transformation. You can now see the real points of the FID by setting lp=0 rp=0, or see the imaginary points by setting lp=0 rp=90. Since linear prediction involves solving a series of equations for appropriate coefficients based on the actual FID, it involves quite a number of parameters and can be somewhat
tricky to optimize (if not optimized properly, or if the data are not amenable, the analysis may simply fail, just like any least-squares fit process may fail to converge). For more complex problems, linear prediction can even be run in a iterative fashion—first extending backward, then forward, and perhaps again backward.

Why Use Linear Prediction
Raw time-domain data acquired during a pulsed NMR experiment can have two flaws:
• Early points in the FID may be distorted due to a host of hardware characteristics, such as preamplifier saturation, probe ringing, and filter non-linearities. Even on a perfect spectrometer, these distortions cannot always be avoided.
• The acquisition time of each FID may have been too short to allow for full decay of the signal, leading to distortion in the Fourier transformed spectrum. Both types of distortions can be solved using linear prediction. This uses the “good” part of the FID to analyze for the frequencies that are present in the signal, and then uses that information to extend the FID either in a reverse direction (to “fix” the first few “bad”
points) or in a forward direction (to eliminate truncation problems, even single “bad” points). Following this process, the “new, improved” FID is then Fourier transformed in the usual way. For more information on the algorithm implemented in the software, and on linear prediction in general, refer to H. Barkhuijsen, R. de Beer, W.M.M.J. Bovée, and D. van Ormondt, J. Magn. Reson., 61, 465-481 (1985).

Solvent Subtraction Filtering
Numerous solvent suppression pulse sequences exist that reduce the signal from a large solvent peak to a level where the desired resonances can be observed. Often, however, experimental solvent suppression does not entirely eliminate an unwanted solvent peak. Digital filtering of the data can further suppress or eliminate a solvent peak. VnmrJ incorporates two algorithms for solvent subtraction by digital filtering:
• In the first, called lfs (low-frequency suppression), a low-pass digital filter is applied to the acquired FID. This filter severely attenuates all signals that lie outside the passband of the filter, leaving only the on-resonance solvent signal and other lowfrequency signals that fall within the filter bandwidth. This filtered FID is then subtracted from the original FID to remove the solvent peak contribution. The Fourier
transform of this FID gives the solvent-subtracted spectrum.
• In the second, called zfs (zero-frequency suppression), the acquired FID is also lowpass filtered, but then the filtered FID is fitted with a polynomial (specified by the parameter ssorder), and the polynomial is subtracted from the original FID. This has the effect of removing from the FID only the signal that is exactly on-resonance. The Fourier transform of this FID produces the solvent-subtracted spectrum. The solvent subtraction parameters ssfilter, sslsfrq, ssntaps, and ssorder control processing.
The parameters ssfilter and ssorder select the processing option as follows:
• The zfs (zero-frequency suppression) option is selected if both ssfilter and ssorder are set to a value other than “Not Used.”
• The lfs (low-frequency suppression) option is selected if ssfilter is set to a value other than “Not Used” and ssorder is set to “Not Used.”
• The zfs and lfs options are both turned off if ssfilter is set to “Not Used.” The characteristics of the low-pass digital filter used with the lfs and zfs options can be modified by changing the parameters ssfilter, sslsfrq, and ssntaps:
• The value of ssfilter specifies the full bandwidth of the low-pass filter applied to the original FID to yield a filtered FID. Its default value is 100 Hz.
• The value of sslsfrq specifies the location of the center of the solvent-suppressed region of the spectrum. Setting sslsfrq to a non-zero value shifts the solvent suppressed region by sslsfrq Hz. Setting sslsfrq to 'n' (the default value) solvent suppresses a region centered about the transmitter frequency.
• The value of ssntaps specifies the number of taps (coefficients) used for the digital filter. The default value is 121 but the value can range from 1 to np/4. The more taps in a filter, the flatter the passband response and the steeper the transition from passband to stopband, giving a more rectangular filter. For the lfs (low-frequency suppression).