Signal Processing: A Mathematical Approach, 2/e (Hardcover)

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.

《信號處理：數學方法》旨在展示讀者所熟悉的數學工具如何應用於應用環境中的信號處理技術。本書假設讀者具有高級本科或研究生水平的數學理解，包括對傅立葉級數、矩陣、概率和統計的熟悉。第二版新增了以下內容：

- 關於卷積和向量DFT、平面波傳播以及BLUE和Kalman濾波器的新章節
- 將傅立葉分析的內容擴展到三個新章節，提供額外的背景信息
- 提供展示數學在遙感中的應用的實際例子

《信號處理：數學方法，第二版》還包含了可用於課堂或實踐的問題，涵蓋了以下主題：

- 單變量和多變量的傅立葉級數和變換
- 應用於聲學和電磁傳播模型、傳輸和發射斷層掃描以及圖像重建的應用
- 取樣和有限數據問題
- 矩陣方法、奇異值分解和數據壓縮
- 投影中的信號和圖像重建的優化技術
- 自相關和功率譜
- 高分辨率方法
- 檢測和最優濾波
- 基於特徵向量的陣列處理和統計濾波、時頻分析和小波方法。