Discrete and Continuous Fourier Transforms
Analysis, Applications and Fast Algorithms

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Language: English

73.59 €

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Discrete and Continuous Fourier Transforms
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· 17.8x25.4 cm · Paperback

214.69 €

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Discrete & continuous Fourier transforms: Analysis, applications & fast algorithms
Publication date:
424 p. · 17.8x25.4 cm · Hardback

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 Transforms: Analysis, Applications and Fast Algorithms presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and FFT algorithms.

This accessible, self-contained book provides meaningful interpretations of essential formulas in the context of applications, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. It comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and many FFT algorithms unified under the frameworks of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text.

Requiring no prior knowledge of Fourier analysis or signal processing, this book supplies the basis for using FFT algorithms to compute the DFT in a variety of application areas.

Preface. Analytical and Graphical Representation of Function Contents. Sampling and Reconstruction of Functions—Part I. The Fourier Series. DFT and Sampled Signals. Sampling and Reconstruction of Functions—Part II. Sampling and Reconstruction of Functions—Part III. The Fourier Transform of a Sequence. The Discrete Fourier Transform of a Windowed Sequence. Discrete Convolution and the DFT. Applications of the DFT in Digital Filtering and Filters. Index Mapping and Mixed-Radix FFTs. Kronecker Product Factorization and FFTs. The Family of Prime Factor FFT Algorithms. On Computing the DFT of Large Prime Length. Bibliography. Index.
Academic and Professional Practice & Development
Eleanor Chu
This self-contained book presents the fundamentals of Fourier analysis and their deployment in signal processing by way of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT) algorithms. It provides meaningful interpretations of essential formulas in the context of applications. The text comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and FFT algorithms unified under the frame works of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text.