Marshall A.G., Verdun F.R. Fourier Transforms in NMR, Optical, and Mass Spectrometry. A User's Handbook

Elsevier, 1990. — 463.This book is offered as a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. Whereas several other books treat either the mathematics or one type of spectroscopy, or offer a collection chapters by several authors, the present monograph offers a unified treatment the three most popular types of FT/spectroscopy, with uniform notation and complete indexing of specialized terms. All mathematics is self-contained, and requires only a knowledge of simple calculus. The main emphasis is on pictures (~200 original illustrations) and physical analogs, with sufficient supporting algebra to enable the reader to enter the literature. Instructive problems offer extensions from the basic treatment. Solutions are given or outlined for all problems.
Because the book aims to inform practicing spectroscopists, non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use mathematically complex variables to represent physically real quantities; interpretation of negative-frequency signals; on-resonance vs. off-resonance response; interpolation (when it helps and when it doesn't); ultimate accuracy discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc.Spectral line shape derived from the motion of a damped mass on a spring
Fourier transforms for analog (continuous) waveforms
Fourier transforms of digital (discrete) waveforms
Fourier Transform Spectrometry: Common Features
Noise
Non-FT methods for proceeding from time- to frequency-domain
Fourier transform ion cyclotron resonance mass spectrometry
Fourier transform nuclear magnetic resonance spectroscopy
FT/interferometry
Epilog: Fourier transforms in other types of spectroscopy
A: Integrals and theorems for FT applications
B: The Dirac δ-functional
C: The FFT algorithm: conceptual basis and program
D: Fourier transform properties and pictorial atlas of Fourier transform pain
E: Physical constants and units