| dc.description.abstract | While the first edition of this textbook was based on a one-year course in
computational physics with a rather limited scope, its extent has been increased
substantially in the third edition, offering the possibility to select from a broader
range of computer experiments and to deepen the understanding of the important
numerical methods. The computer experiments have always been a central part of
my concepts for this book. Since Java applets, which are very convenient otherwise,
have become more or less deprecated and their usage in a browser is no longer
recommended for security issues, I decided to use standalone Java programs instead
and to rewrite all of the old examples. These can also been edited and compiled
with the “netbeans” environment and offer the same possibilities to generate a
graphical user interface in short time.
The major changes in the third edition are as follows.
In the first part, a new chapter is devoted to the time-frequency analysis of
experimental data. While the classical Fourier transform allows the calculation
of the spectrum of a stationary signal, it is not so useful for nonstationary signals
with significant variation of the momentaneous frequency distribution. Application
of the Fourier transformation to short time windows, a method which is known as
short-time Fourier transformation (STFT), allows analyzing the frequency content
of a signal as a function of time. Good time resolution, of course, always comes
together with a loss in frequency resolution (this is well known as “uncertainty
principle”). The STFT method uses the same window for the whole spectrum,
therefore the absolute time and frequency resolution is the same for low- and
high-frequency components and the time resolution is limited by the period of the
lowest frequencies of interest. Analysis of a signal with wavelets, on the other hand,
uses shorter windows for the higher frequencies and keeps the relative frequency
resolution constant while increasing the time resolution of the high-frequency
components. The continuous wavelet transform can be very time consuming since it
involves a convolution integral and is highly redundant. The discrete wavelet transform uses a finite number of orthogonal basis function and can be performed
much faster by calculating scalar products. It is closely related to multiresolution
analysis which analyzes a signal in terms of a basic approximation and details
of increasing resolution. Such methods are very popular in signal processing,
especially of audio and image data but also in medical physics and seismology. The
principles of the construction of orthogonal wavelet families are explained in detail,
but without too many mathematical proofs. Several popular kinds of wavelets are
discussed, like those by Haar, Meyer and Daubechies and their application is
explored in a series of computer experiments. | en_US |
