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, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. 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.