Mastering the Discrete Fourier Transform in One,
Two or Several Dimensions:
Pitfalls and Artifacts
Welcome to the Internet site of the DFT book by Isaac Amidror, a new companion to the
two previous volumes by the same author which dealt with the theory
of the moiré phenomenon.
The discrete Fourier transform (DFT) is an extremely useful tool that finds application
in many different disciplines. However, its use requires caution due to various pitfalls and
artifacts that await the unaware users and risk to mislead them in the interpretation of the
results. The aim of this book is to explain the DFT and its various artifacts and pitfalls,
and to show how to avoid these artifacts (whenever possible), or at least how to recognize
them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts
and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of
information for the widest possible range of DFT users. Special attention is given to the one
and two dimensional cases due to their particular importance, but the discussion covers the
general multidimensional case, too.
- The material presented in this book includes a wide range of subjects, ranging from the
aliasing and leakage phenomena to less widely known topics such as symmetry related issues
and the DFT artifacts that may result thereof, or the influence of the various possible types
of data extension on the DFT results.
- This book intends to attract the reader's attention to the many possible pitfalls and
sources of error in the use of DFT, including potential errors due to the different CFT or DFT
definitions being used in different books and software packages, the need for input and output
data reorganizations, etc. It shows the users how to correctly interpret the DFT results they obtain,
how to distinguish between true spectral contents and the various artifacts that are only due to DFT,
how to place the true unit values along the axes when plotting the DFT results, and many other
practical issues that are often acquired only through the user's own experience, sometimes simply
by trial and error.
- This book is written in an informal style using a pictorial, intuitive approach which is
supported by mathematics. It intentionally avoids a purist's approach based on
theorems and proofs, and puts an emphasis on the intuitive understanding of the issues
- Just like the author's previous books on the theory of the moiré
phenomenon, this volume, too, contains a large number of illustrative examples and figures,
some of which are visually fascinating and even spectacular. It contains 375 pages, including a
detailed glossary and more than 140 figures.
The present book is intended for scientists, engineers, students and any readers who wish
to widen their knowledge of the DFT and its practical use. This book will also be very
useful for “naive” users from various scientific or technical disciplines who have to
use the DFT for their respective applications. The prerequisite mathematical background
is limited to an elementary familiarity with calculus and with the continuous and
discrete Fourier theory.
Springer, CIVI #43 ISBN 978-1-4471-5166-1
See for yourself ...
Mastering the Discrete Fourier Transform in One, Two or Several Dimensions: Pitfalls
and Artifacts by I. Amidror
ISBN 978-1-4471-5166-1 (hardcover)
Last modified: 2014/12/16