Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform

A companion volume to Weaver's Applications of Discrete and Continuous Fourier Analysis (Wiley, 1983). Addresses the theoretical and analytical aspects of Fourier analysis, including topics usually found only in more advanced treatises. Provides background information before going on to cover such topics as existence of the inner product, distribution theory, Fourier series representation of complex functions, properties and behavior of the Fourier transform, Fourier transform of a distribution, physical interpretation of convolution, the fast Fourier transform, sampling a function, and much more. Includes exercises, problems, applications, over 150 illustrations, and a Fourier transform FORTRAN subroutine.

An applications oriented, introductory text covering the concepts and properties of Fourier Analysis. Emphasizes applications to real scientific and engineering problems. Defines the Fourier series, Fourier transform, and discrete Fourier transform. Includes over 200 illustrations.

The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

Diploma Thesis from the year 2006 in the subject Computer Science - Applied, grade: 2.0, University of Salzburg (Department of Computer Sciences), course: Natural Computation, 36 entries in the bibliography, language: English, abstract: This thesis presents techniques to detect mental blocks in humans based on the physiological parameters skin potential and skin resistance. We examine physiological measures from the Musico Cause and Effect study of the Science Network for Man and Music at the University of Music and Dramatic Arts, Mozarteum Salzburg. The existing digital signal analysis tool AIDA used to process the physiological data has been replaced by the Dynalyzer developed by the author with considerable improvements in accuracy and performance. We present fundamentals of digital signal processing, outline the measurement of physiological data, and discuss characteristics of mental blocks. We suggest several criteria for the detection of mental blocks based on characteristic features of the physiological time series in the time and/or frequency domain. In first experiments the potential of these criteria is evaluated by applying them to actual physiological data of a test subject. As no ground truth on the occurrence of mental blocks is available, the experimental results can only be an indicator for the quality of the detection of mental blocks. Further experiments are conducted with data from the Vienna determination test assessing the reactive stress tolerance and attention deficits of human test subjects.

The fourier transform; Fourier transform properties; Convolution and correlation; Fourier series and sampled waveforms; The discrete fourier transform; Discrete convolutiion and correlation; Applying the discrete fourier transform.

The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come.

An exploration of the basics of signal theory, and of both the time-and frequency-domain analyses of systems. The discrete and continuous-time cases are presented in parallel, at times in a two-column format for ease of comparison. Separate chapters examine applications in signal processing, digital filtering, communication systems, and automatic c.