Mathematics of Signal Processing: A First Course

✍ Scribed by Byrne C.L.

• Tongue: English
• Leaves: 410
• Category: Library

✦ Synopsis

Учебное пособие
Издательство: Department of Mathematical Sciences,
University of Massachusetts, Lowell, 2013. - 410 стр.
Язык: Английский.

The main goals of this first course are to present the most important ideas, techniques and methods, to describe how they relate to one another, and to illustrate their uses in several applications.
This text is designed to provide the necessary mathematical background to understand and employ signal processing techniques in an applied environment. The emphasis is on a small number of fundamental problems and essential tools, as well as on applications. Certain topics that are commonly included in textbooks are touched on only briefly or in exercises or not mentioned at all.
Topics discussed include the following: Fourier series and transforms in one and several variables; applications to acoustic and EM 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; eigenvector-based methods for array processing and statistical filtering.

I Introduction
Preface
Urn Models in Remote Sensing

II Fundamental Examples
Transmission and Remote Sensing- I

III Signal Models
Undetermined-Parameter Models
Complex Numbers
Complex Exponential Functions
Transmission and Remote Sensing- II

IV Fourier Methods
Fourier Analysis
Properties of the Fourier Transform
The Fourier Transform and Convolution Filtering
Infinite Sequences and Discrete Filters
Convolution and the Vector DFT
The Fast Fourier Transform (FFT)
Plane-wave Propagation

V Nonlinear Models
Random Sequences
Classical and Modern Methods
Entropy Maximization
Eigenvector Methods in Estimation
The IPDFT

VI Wavelets
Analysis and Synthesis
Ambiguity Functions
Time-Frequency Analysis
Wavelets

VII Estimation and Detection
The BLUE and The Kalman Filter
Signal Detection and Estimation

VIII Appendices
Inner Products
Reverberation and Echo Cancellation
Using Prior Knowledge to Estimate the Fourier Transform
The Vector Wiener Filter
Wiener Filter Approximation
Fourier Series and Analytic Function
Inverse Problems and the Laplace Transform
Matrix Theory
Matrix and Vector Differentiation
Compressed Sensing
Transmission Tomography I
Transmission Tomography II

Bibliography
Index

✦ Subjects

Приборостроение;Обработка сигналов