Edition |
Second edition. |
Description |
xviii, 242 pages ; 24 cm. |
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text txt rdacontent |
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unmediated n rdamedia |
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volume nc rdacarrier |
Series |
Undergraduate lecture notes in physics, 2192-4791 |
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Undergraduate lecture notes in physics.
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Bibliography |
Includes bibliographical references (page 237) and index. |
Contents |
Fourier series. Fourier series ; Theorems and rules ; Parital sums, Bessel's inequality, Parseval's equation ; Gibb's phenomenon -- Continuous Fourier transformation. Continuous Fourier transformation ; Theorems and rules ; Convolution, cross correlation, autocorrelation, Parseval's theorem ; Fourier transformation of derivatives ; Pitfalls -- Window functions. The rectangular window ; The triangular window (Fejer window) ; The cosine window ; The cos²-Window (Hanning) ; The Hamming window ; The triplet window ; The Gauss window ; The Kaiser-Bessel window ; The Blackman-Harris window ; Overview of the window functions ; Windowing or convolution? -- Discrete fourier transformation. Discrete Fourier transformation ; Theorems and rules ; Convolution, cross correlation, autocorrelation, Parseval's theorem ; The sampling theorem ; Data mirroring ; How to get rid of the "Straight-jacket" periodic continuation? By using zero-padding! ; Fast fourier transformation (FFT) -- Data streams and fractional delays. Fractional delays ; Non-recursive algorithms ; Stabiltiy of recursive algorithms ; Thiran's all-pass filter for N = 1 -- Tomography : backprojection of filtered projections. Projection ; Backprojection of filtered projections -- Appendix: Solutions. |
Summary |
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on windoe functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions -- Book jacket. |
Subject |
Fourier transformations.
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Fourier transformations. (OCoLC)fst00933413
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(DE-601)106327925 (DE-588)4018014-1 Fourier-Transformation
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ISBN |
9783319169842 (paperback) |
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331916984X (paperback) |
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