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Fourier Transforms In Spectroscopy - Kauppinen J, Angielskie techniczne
[ Pobierz całość w formacie PDF ]Fourier Transforms in Spectroscopy
. J. Kauppinen, J. Partanen
Copyright © 2001 Wiley-VCH Verlag GmbH
ISBNs: 3-527-40289-6 (Hardcover); 3-527-60029-9 (Electronic)
Jyrki Kauppinen, Jari Partanen
Fourier Transforms in Spectroscopy
Fourier Transforms in Spectroscopy
. J. Kauppinen, J. Partanen
Copyright © 2001 Wiley-VCH Verlag GmbH
ISBNs: 3-527-40289-6 (Hardcover); 3-527-60029-9 (Electronic)
Jyrki Kauppinen, Jari Partanen
Fourier Transforms
in Spectroscopy
Berlin Weinheim New York Chichester
Brisbane Singapore Toronto
Fourier Transforms in Spectroscopy
. J. Kauppinen, J. Partanen
Copyright © 2001 Wiley-VCH Verlag GmbH
ISBNs: 3-527-40289-6 (Hardcover); 3-527-60029-9 (Electronic)
Authors:
Prof. Dr. Jyrki Kauppinen
Department of Applied Physics
University of Turku
University of Turku
Finland
Finland
e-mail: jyrki.kauppinen@utu.fi
e-mail: jari.partanen@utu.fi
This book was carefully produced. Nevertheless, authors and publisher do not warrant the
information contained therein to be free of errors. Readers are advised to keep in mind that
statements, data, illustrations, procedural details or other items may inadvertently be
inaccurate.
1st edition, 2001
with 153 figures
Library of Congress Card No.: applied for
A catalogue record for this book is available from the British Library.
Die Deutsche Bibliothek - CIP Cataloguing-in-Publication-Data
A catalogue record for this publication is available from Die Deutsche Bibliothek
ISBN 3-527-40289-6
© WILEY-VCH Verlag Berlin GmbH, Berlin (Federal Republic of Germany), 2001
Printed on acid-free paper.
All rights reserved (including those of translation in other languages). No part of this book may be
reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or
translated into machine language without written permission from the publishers. Registered
names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be
considered unprotected by law.
Printing: Strauss Offsetdruck GmbH, D-69509 Mörlenbach. Bookbinding: J. Schäffer GmbH &
Co. KG, D-67269 Grünstadt.
Printed in the Federal Republic of Germany.
WILEY-VCH Verlag Berlin GmbH
Bühringstraße 10
D-13086 Berlin
Federal Republic of Germany
Department of Applied Physics
Dr. Jari Partanen
Fourier Transforms in Spectroscopy
. J. Kauppinen, J. Partanen
Copyright © 2001 Wiley-VCH Verlag GmbH
ISBNs: 3-527-40289-6 (Hardcover); 3-527-60029-9 (Electronic)
Preface
How much should a good spectroscopist know about Fourier transforms? How well should a
professional who uses them as a tool in his/her work understand their behavior? Our belief
is, that a profound insight of the characteristics of Fourier transforms is essential for their
successful use, as a superficial knowledge may easily lead to mistakes and misinterpretations.
But the more the professional knows about Fourier transforms, the better he/she can apply all
those versatile possibilities offered by them.
On the other hand, people who apply Fourier transforms are not, generally, mathemati-
cians. Learning unnecessary details and spending years in specializing in the heavy math-
ematics which could be connected to Fourier transforms would, for most users, be a waste
of time. We believe that there is a demand for a book which would cover understandably
those topics of the transforms which are important for the professional, but avoids going into
unnecessarily heavy mathematical details. This book is our effort to meet this demand.
We recommend this book for advanced students or, alternatively, post-graduate students
of physics, chemistry, and technical sciences. We hope that they can use this book also
later during their career as a reference volume. But the book is also targeted to experienced
professionals: we trust that they might obtain new aspects in the use of Fourier transforms by
reading it through.
Of the many applications of Fourier transforms, we have discussed Fourier transform
spectroscopy (FTS) in most depth. However, all the methods of signal and spectral processing
explained in the book can also be used in other applications, for example, in nuclear magnetic
resonance (NMR) spectroscopy, or ion cyclotron resonance (ICR) mass spectrometry.
We are heavily indebted to Dr. Pekka Saarinen for scientific consultation, for planning
problems for the book, and, finally, for writing the last chapter for us. We regard him as a
leading specialist of linear prediction in spectroscopy. We are also very grateful to Mr. Matti
Hollberg for technical consultation, and for the original preparation of most of the drawings
in this book.
Jyrki Kauppinen and Jari Partanen
Turku, Finland, 13th October 2000
Fourier Transforms in Spectroscopy
. J. Kauppinen, J. Partanen
Copyright © 2001 Wiley-VCH Verlag GmbH
ISBNs: 3-527-40289-6 (Hardcover); 3-527-60029-9 (Electronic)
Contents
1Basic definitions
11
1.1
Fourier series . . . .............................. 11
1.2
Fourier transform ............................... 14
1.3
Dirac’s delta function . . . . . ........................ 17
2General properties of Fourier transforms
23
2.1
Shift theorem . . . .............................. 24
2.2
Similarity theorem . . . . . . . ....................... 25
2.3
Modulation theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4
Convolution theorem . . . . . . ....................... 26
2.5
Power theorem . . . ............................. 28
2.6
Parseval’s theorem . . . . . . ........................ 29
2.7
Derivative theorem . . . . . . ........................ 29
2.8
Correlation theorem . . . . . . ........................ 30
2.9
Autocorrelation theorem . . . . ....................... 31
3Discrete Fourier transform
35
3.1
Effect of truncation . . . . . . . ....................... 36
3.2
Effect of sampling . .............................. 39
3.3
Discrete spectrum............................... 43
4Fast Fourier transform (FFT)
49
4.1
Basis of FFT . . . . .............................. 49
4.2
Cooley–Tukey algorithm . . . . . ...................... 54
4.3
Computation time . .............................. 56
5Other integral transforms 61
5.1 Laplace transform . . . . . . . ........................ 61
5.2 Transfer function of a linear system . . ................... 66
5.3
z
transform . ................................. 73
6Fourier transform spectroscopy (FTS)
77
6.1
Interference of light . . . . . . ........................ 77
6.2
Michelson interferometer . . . ........................ 78
6.3
Sampling and truncation in FTS ....................... 83
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