Discrete and Continuous Fourier Transforms

This accessible, self-contained book presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and 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

Eleanor Chu

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.