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.

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.