JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1991. VOL. 6 101 Book Review Fourier Tansforms in NMR Optical and Mass Spectrometry Alan G. Marshall and Francis R. Verdun. Pp. xvi+210. Elsevier. 1990. Price $107.25 Df1222.00 (hardback); $46.25 Df195.00 (paperback). ISBN 0 444 87360 0 (hardback); 0 444 87412 7 (paperback). The object of this book is to present a unified treatment of the three most common types of Fourier transform (FT) spectrometry-optical mass (MS) and nuclear magnetic resonance (NMR). This unified treatment extends over six chap- ters and the three separate forms are covered in the last three chapters. Specifi- cally Chapter 1 introduces fundamental line shapes by discussing the complex amplitude of forced oscillations of a damped harmonic oscillator. The reader is then introduced to the usual FT pairs the convolution and shift theorems the effects of discrete sampling and phase correction in Chapters 2 and 3.Some common features of the three spectrome- tries (the mutiplex principle resolution modulation ell-.) are discussed in Chapter 4. The other two general chapters Chap- ters 5 and 6 cover respectively noise and non-FT methods of signal handling (Laplace transforms auto-regression and auto-correlation and maximum entropy). After the two chapters on FT ion cyclo- tron resonance MS and FT-NMR we reach optical spectrometry under the title of FT-interferometry . From the point of view of an optical spectroscopist which is the background against which this review is written the book does not offer the easiest way into the subject.Chapter 1 in particular seems to add unnecessary confusion. When the damped oscillator concept is applied to a bound electron the real part of the complex amplitude gives rise to disper- sion while the imaginary part gives ab- sorption. In the very next chapter however we find the absorption spec- trum referred to as real and the disper- sion spectrum as imaginary. To add confusion the real and imaginary parts of the oscillator amplitude are designated by .r’ and Y’ as if they were the first and second time derivatives. The mathematical treatment in Chap- ters 2 and 3 is fairly standard but I per- sonally find it harder to follow than a ‘classic’ such as Bracewell’s ‘The Fourier transform and its applications’. One difficulty for optical spectroscopists is the exclusive use of the time-frequency Fourier pair for which causality does not allow signals at KO.The path differenc- es-wavenumber pair (s o) for which signals can be acquired at .\-<O is not in- troduced until Chapter 9. Thus the use of a short two-sided section of the interfero- gram to determine phase and then correct it the method commonly used in optical spectrometry does not appear in the dis- cussion of phase correction in Chapter 4. A further consequence which is a curio- sity to optical spectroscopists is the use of zero filling to recover the complete spectral information. As the above example indicates some of the general features of FT spectro- metry discussed in the book are much more relevant to MS and NMR than to optical spectrometry.Another example is the discussion of polarization quadrature excitation and heterodyning that occupies most of the second half of Chapter 4.102 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 199 1 VOL. 6 This partial specialization would matter less if the reader had a clearer idea of the origin of the input signals and the infor- mation required from the FT output in . each instance. It is a pity that Chapter 1 has not been used to give a brief explana- tion of each of the three experimental techniques so as to provide this back- ground. On the credit side there is a much fuller discussion of noise than is offered by most books and Chapter 6 presents a useful introduction to general methods of signal handling (transfer functions auto- regression maximum entropy etc.) which is not normally found in texts on spectrometric methods. Finally there are both positive and negative points to be made about the pres- entation. The liberal use of diagrams and the sections on problems and hints for so- lutions at the end of each chapter are plus points. On the minus side the format of both diagrams and text makes them rather unnecessarily difficult to read; the dia- grams have a cluttered appearance and the captions of the figures and tables are not easily distinguished from the text. Anne P. Thorne Imperial College of Science Technology and Medicine London UK