Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics—including familiarity with Fourier series, matrices, probability, and statistics—this Second Edition:
- Contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters
- Expands the material on Fourier analysis to three new chapters to provide additional background information
- Presents real-world examples of applications that demonstrate how mathematics is used in remote sensing
Featuring problems for use in the classroom or practice, Signal Processing: A Mathematical Approach, Second Edition covers topics such as Fourier series and transforms in one and several variables; applications to acoustic and electro-magnetic propagation models, transmission and emission tomography, and image reconstruction; sampling and the limited data problem; matrix methods, singular value decomposition, and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; detection and optimal filtering; and eigenvector-based methods for array processing and statistical filtering, time-frequency analysis, and wavelets.
Table of Contents
Introduction. Fourier Series and Fourier Transforms. Remote Sensing. Finite-Parameter Models. Transmission and Remote Sensing. The Fourier Transform and Convolution Filtering. Infinite Sequences and Discrete Filters. Convolution and the Vector DFT. Plane-Wave Propagation. The Phase Problem. Transmission Tomography. Random Sequences. Nonlinear Methods. Discrete Entropy Maximization. Analysis and Synthesis. Wavelets. The BLUE and the Kalman Filter. Signal Detection and Estimation. Appendices.
Charles L. Byrne
"The second edition of this book further confirms the skill of its author to combine mathematical rigor with intuitive understanding. ... All chapters are carefully structured such that the reader can make easily an image on the main ideas of each topic, not only from the mathematical point of view but also regarding intuitive interpretations and applications. In fact, the book can be a very good course for advanced undergraduates who will find in it a kind of handbook of connections between mathematical concepts and applications in signal processing. ... The book is worth reading not only by students but also by people wishing to have a broad image on signal processing in its intrinsic relationship with mathematics."
—Liviu Goras (Iasi), from Zentralblatt MATH 1321 – 1