Software for Fourier Transforms

Processing Software for Fourier Transform Spectroscopies Transparent re-mapping... 

The following is the forward Fourier transform routine F0UR1 from J. C. Sprott, "Numerical Recipes Routines and Examples in BASIC", Cambridge University Press, Copyright (C) 1991 by Numerical Recipes Software. Used by permission. Use of this routine other than as an integral part of the present book requires an additional license from Numerical Recipes Software. Further distribution is prohibited. The routine has been modi- fied to yield double-precision results, and to conform to the standard mathematical convention for Fourier transformation. 

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

The advancement of >400 MHz NMR instruments with spin decoupling and Fourier transform software now allows identification of individual olefinic protons of nanogram carotenoids53. We have shown two examples (lycopene and capsantin) for which the chemical shifts have been employed in the assignment of relative configuration49. As for review of the 13C NMR of carotenoids, Englert in 198154 gave information especially on the position of the cis double bonds in a polyene chain. 

Selected topics in Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry instrumentation are discussed in depth, and numerous analytical application examples are given. In particular, optimization ofthe single-cell FTMS design and some of its analytical applications, like pulsed-valve Cl and CID, static SIMS, and ion clustering reactions are described. Magnet requirements and the software used in advanced FTICR mass spectrometers are considered. Implementation and advantages of an external differentially-pumped ion source for LD, GC/MS, liquid SIMS, FAB and LC/MS are discussed in detail, and an attempt is made to anticipate future developments in FTMS instrumentation. 

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