- Email: [email protected]
Spectroscopy and the Fourier Transform
62
trends in analytical chemistry, vol. 16, no. 1, 1997
[ 161 M. Chastrette, M. Rajzmann, M. Chanon and K.F. Purcell, J. Am. Chem. Sot., 107 ( 1985) 1. [ 171 0. Pytela, Collect. Czech. Chem. Commun., 55 ( 1990) 644. [ 181 M.J. Kamlet and R.W. Taft, Acta Chem. Stand. Ser. B, 39 (1985) 611. [ 191 E. Casassas, G. Fonrodona, A. de Juan and R. Tamer, Chemom. Intell. Lab. Syst., 12 ( 1991) [ 201 E:H. [ 211 [ 22 ] [ 23 ]
[ 241 [ 25 ]
Abraham, Pure Appl. Chem., 65 ( 1993) 2503. L.C. Tan and P.W. Carr, J. Chromatogr. A, 656 (1993) 521 P. Meyer and G. Maurer, Ind. Eng. Chem. Res., 34 (1995) 373. M. Forma, R. Leardi, C. Armanino and S. Lanteri, PARVUS, an Extendable Package of Programs for Data Exploration, Classification and Correlation, Elsevier, Amsterdam, 1988. P.H.A. Sneath, J. Gen. Microbial., 17 (1957) 201. P.H.A. Sneath and R.R. Sokal, Numerical Taxonomy: The Principles and Practice of Numerical
[ 26 ] [ 271 [ 281
[ 291
[ 301 [ 3 1] [ 321 [ 33 ]
Classification, Freeman, San Francisco, CA, 1973. G.N. Lance and W.T. Williams, Aust. Comput. J., 1 (1967) 15. J.H. Ward, J. Am. Stat. Assoc., 58 (1963) 236. D. Wishart, An Improved Multivariate ModeSeeking Cluster Method, RSS Conference on Multivariate Analysis and its Applications, Hull, 1973. D. Wishart, in A.J. Cole (Editor), Mode Analysis in Numerical Taxonomy, Academic Press, New York, 1969. D. Wishart, Clustan User Manual, University of St. Andrews, Edinburgh, 4th edn., 1987. L.R. Snyder, J. Chromatogr., 92 ( 1974) 223. L.R. Snyder, P.W. Carr and S.C. Rutan. J. Chromatogr. A, 656 (1993) 537. E. Casassas, N. Dominguez, G. Fonrodona and A. de Juan, Anal. Chim. Acta, 283 (1993) 548.
The authors are at the Departament de Quimica Analitica, Universita t de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
book reviews Fourier transform spectroscopy Spectroscopy and the Fourier Transform, by Ron Williams, VCH, Weinheim, 7996, Price DM 108, ISBN
1-56081-576-O
The author has had the potentially good idea of illustrating the principles and practice of Fourier transform spectroscopy by, as he puts it, “an interactive tutorial”, requiring the use of a spreadsheet to generate and graph the functions discussed. After three chapters demonstrating Fourier series, Fourier transforms and a few other topics such as convolution and correlation there is a short chapter on the mathematical background and then three chapters on Fourier transform specrometric applications - infrared optical (IR), nuclear magnetic resonance (NMR) and mass spectroscopy (MS). Evidently the reader is expected to have very little mathematical background, with no previous knowledge of Fourier series or of complex num-
bers; most of Chapter 2, for example, is devoted to showing that a square wave and a Gaussian can be represented by Fourier series. A somewhat patronising approach is adopted to this hypothetical semi-innumerate reader - for example, the explanation of phase: “In its simplest definition phase is the relative amounts of sine and cosine components at each frequency and is expressed in radians. (Doesn’t make a lot of sense, does it?)” Assuming that the demand for a tutorial at this level exists, the next question is how well it succeeds. The demonstrations are based on Microsoft Excel, and the spreadsheets on the disc that comes with the book are also specific to Excel. The author suggests that the demonstrations can also be used with othe commercial spreadsheets, but I suspect this would be difficult because the instructions given are so very specific (“enter the following formula into cell Al ... press Enter ... hold down the shift key while
clicking in cell Dl ... choose Fill Right from the Edit menu ...“) and tend to mask what is actually going on. An additional problem is that the x-axis is always labelled by row number, with nothing to show whether it represents frequency or time. A statement of each algorithm, with a brief description of its functions, before the instruction set would surely enhance the tutorial function and increase the usefulness to users of different spreadsheets. The arrangement of the book, in which the mathematical background follows the spreadsheet demonstrations, has two disadvantages in my view. The first is that the reader is following a set of instructions without The understanding their purpose. second is that concepts such as phase and the imaginary part of the transform are encountered before complex numbers are explained. If it is actually the case that users of FTS need an explanation of \/(-I), surely they need it when they are first exposed to imaginary numbers. The mathematical background chapter, when one finally reaches it, is
trends in analytical chemistry, vol. 16, no. 1, 1997
[ 161 M. Chastrette, M. Rajzmann, M. Chanon and K.F. Purcell, J. Am. Chem. Sot., 107 ( 1985) 1. [ 171 0. Pytela, Collect. Czech. Chem. Commun., 55 ( 1990) 644. [ 181 M.J. Kamlet and R.W. Taft, Acta Chem. Stand. Ser. B, 39 (1985) 611. [ 191 E. Casassas, G. Fonrodona, A. de Juan and R. Tamer, Chemom. Intell. Lab. Syst., 12 ( 1991) [ 201 E:H. [ 211 [ 22 ] [ 23 ]
[ 241 [ 25 ]
Abraham, Pure Appl. Chem., 65 ( 1993) 2503. L.C. Tan and P.W. Carr, J. Chromatogr. A, 656 (1993) 521 P. Meyer and G. Maurer, Ind. Eng. Chem. Res., 34 (1995) 373. M. Forma, R. Leardi, C. Armanino and S. Lanteri, PARVUS, an Extendable Package of Programs for Data Exploration, Classification and Correlation, Elsevier, Amsterdam, 1988. P.H.A. Sneath, J. Gen. Microbial., 17 (1957) 201. P.H.A. Sneath and R.R. Sokal, Numerical Taxonomy: The Principles and Practice of Numerical
[ 26 ] [ 271 [ 281
[ 291
[ 301 [ 3 1] [ 321 [ 33 ]
Classification, Freeman, San Francisco, CA, 1973. G.N. Lance and W.T. Williams, Aust. Comput. J., 1 (1967) 15. J.H. Ward, J. Am. Stat. Assoc., 58 (1963) 236. D. Wishart, An Improved Multivariate ModeSeeking Cluster Method, RSS Conference on Multivariate Analysis and its Applications, Hull, 1973. D. Wishart, in A.J. Cole (Editor), Mode Analysis in Numerical Taxonomy, Academic Press, New York, 1969. D. Wishart, Clustan User Manual, University of St. Andrews, Edinburgh, 4th edn., 1987. L.R. Snyder, J. Chromatogr., 92 ( 1974) 223. L.R. Snyder, P.W. Carr and S.C. Rutan. J. Chromatogr. A, 656 (1993) 537. E. Casassas, N. Dominguez, G. Fonrodona and A. de Juan, Anal. Chim. Acta, 283 (1993) 548.
The authors are at the Departament de Quimica Analitica, Universita t de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
book reviews Fourier transform spectroscopy Spectroscopy and the Fourier Transform, by Ron Williams, VCH, Weinheim, 7996, Price DM 108, ISBN
1-56081-576-O
The author has had the potentially good idea of illustrating the principles and practice of Fourier transform spectroscopy by, as he puts it, “an interactive tutorial”, requiring the use of a spreadsheet to generate and graph the functions discussed. After three chapters demonstrating Fourier series, Fourier transforms and a few other topics such as convolution and correlation there is a short chapter on the mathematical background and then three chapters on Fourier transform specrometric applications - infrared optical (IR), nuclear magnetic resonance (NMR) and mass spectroscopy (MS). Evidently the reader is expected to have very little mathematical background, with no previous knowledge of Fourier series or of complex num-
bers; most of Chapter 2, for example, is devoted to showing that a square wave and a Gaussian can be represented by Fourier series. A somewhat patronising approach is adopted to this hypothetical semi-innumerate reader - for example, the explanation of phase: “In its simplest definition phase is the relative amounts of sine and cosine components at each frequency and is expressed in radians. (Doesn’t make a lot of sense, does it?)” Assuming that the demand for a tutorial at this level exists, the next question is how well it succeeds. The demonstrations are based on Microsoft Excel, and the spreadsheets on the disc that comes with the book are also specific to Excel. The author suggests that the demonstrations can also be used with othe commercial spreadsheets, but I suspect this would be difficult because the instructions given are so very specific (“enter the following formula into cell Al ... press Enter ... hold down the shift key while
clicking in cell Dl ... choose Fill Right from the Edit menu ...“) and tend to mask what is actually going on. An additional problem is that the x-axis is always labelled by row number, with nothing to show whether it represents frequency or time. A statement of each algorithm, with a brief description of its functions, before the instruction set would surely enhance the tutorial function and increase the usefulness to users of different spreadsheets. The arrangement of the book, in which the mathematical background follows the spreadsheet demonstrations, has two disadvantages in my view. The first is that the reader is following a set of instructions without The understanding their purpose. second is that concepts such as phase and the imaginary part of the transform are encountered before complex numbers are explained. If it is actually the case that users of FTS need an explanation of \/(-I), surely they need it when they are first exposed to imaginary numbers. The mathematical background chapter, when one finally reaches it, is