信号谱分析：理论与方法
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收藏 21.38MB PDF 举报 "《现代信号谱分析》是Petre Stoica和Randolph Moses合著的一本专业书籍，详细探讨了信号谱分析的各种方法和技术。本书分为六个主要章节，涵盖从基本概念到高级分析技术，包括非参数化方法、有理谱估计的参数化方法、线谱估计的参数化方法、滤波器组方法以及空域方法。此外，书中还包含三个附录，提供线性代数、Cramer-Rao界分析工具和模型阶数选择方法等辅助知识。"
本书首先介绍了信号谱分析的基本概念，包括确定信号的能量谱密度和随机信号的功率谱密度，以及它们的性质。谱估计问题作为核心内容，书中详细阐述了如何进行谱估计，并给出了补充内容和习题以供深入学习。
在非参数化方法章节，作者讲解了周期图和相关图法，利用快速傅里叶变换(FFT)计算周期图，并讨论了Blackman-Tukey方法及窗函数设计的重要问题。此外，还介绍了一些改进的周期图方法，帮助读者理解这些方法的优缺点。
有理谱估计的参数化方法章节主要围绕ARMA过程展开，包括AR和MA信号的处理，如Yule-Walker方程的阶递推解法。同时，扩展到了多变量ARMA信号，提供了丰富的理论和实践应用。
线谱估计的参数化方法章节聚焦于噪声环境中的正弦信号模型，探讨了非线性最小二乘方法，以及高阶Yule-Walker方法、Pisarenko和MUSIC方法、最小模方法和ESPRIT方法等，这些方法在信号分离和频率估计中有着广泛的应用。
滤波器组方法章节讨论了如何使用滤波器组来解释和改进周期图，提到了Capon方法，并进一步解释了滤波器组在周期图分析中的作用。
空域方法章节则涉及阵列信号处理，介绍了阵列模型，非参数化和参数化方法，这在多天线通信和雷达系统中具有重要意义。
附录部分提供了线性代数和矩阵分析、Cramer-Rao界分析以及模型阶数选择方法的基础知识，有助于读者深入理解正文中的理论和算法。
《现代信号谱分析》是一本全面而深入的教材，适合对信号处理、通信工程和相关领域感兴趣的读者，为理解和应用现代谱分析技术提供了坚实的基础。
Preface
xvii
focuses on continuous spectral models (Autoregressive Moving Average (ARMA) models and
their AR and MA special cases), while Chapter 4 focuses on discrete spectral models (sinusoids
in noise). We have placed the filter-bank methods in Chapter 5, after Chapters 3 and 4, mainly
because the Capon estimator has interpretations both
as
an averaged AR spectral estimator and
as
a matched filter for line-spectral models, and we need the background
of
Chapters 3
and
4 to
develop these interpretations. The data-independent filter-bank techniques in Sections
5.1-5.4
can
equally well be covered directly following Chapter
2,
if
de~ired.
Chapter 6 considers the closely related problem
of
spatial spectral estimation in the context
of
array signal processing. Both nonparametric (beamforming) and parametric methods are consid-
ered, and both are tied into the temporal spectral estimation techniques considered in Chapters
2,
4, and 5.
The bibliography contains both modem and classical references (ordered both alphabetically
and by subject). We include many historical references
as
well, for those interested in tracing the
early developments
of
spectral analysis. However, spectral analysis is a topic with contriblltions
from many diverse fields, including electrical and mechanical engineering, astronomy, biomedical
spectroscopy, geophysics, mathematical statistics, and
econometrics-to
name a few. As such,
any attempt to document the historical development
of
spectral analysis accurately is doomed to
failure. The bibliography reflects our own perspectives, biases, and limitations; there is no doubt
that the list is incomplete, but we hope that it gives the reader an appreciation
of
the breadth and
diversity of the spectral analysis field.
The background needed for this text includes a basic knowledge of linear algebra, discrete-
time linear systems, and introductory discrete-time stochastic processes (or time series). A basic
understanding
of
estimation theory is helpful, though not required. Appendix A develops most
of
the needed background results on matrices and linear algebra, Appendix B gives a tutorial intro-
duction to the Cramer-Rao bound, and Appendix C develops the theory of model order selection.
We
have included concise definitions and descriptions
of
the required concepts and results where
needed. Thus, we have tried to make the text
as
self-contained
as
possible.
We
are indebted
to
Jian Li and Lee Potter for adopting a former version of the text in
their spectral estimation classes, for their valuable feedback, and for contributing to this book in
several other ways. We would like to thank Torsten Soderstrom, for providing the initial stimulus
for preparation
of
lecture notes that led to the book, and Hung-Chih Chiang, Peter Handel, Ari
Kangas, Erlendur Karlsson, and Lee Swindlehurst, for careful proofreading and comments and
for many ideas on and early drafts
of
the computer problems. We are grateful to Mats Bengtsson,
Tryphon Georgiou, K.V.S. Hari, Andreas Jakobsson, Erchin Serpedin, and A.ndreas Spanias for
comments and suggestions that helped us eliminate some inadvertencies and typographical errors
from the previous edition
of
the book.
We
also wish to thank Wallace Anderson, Alfred Hero,
Ralph Hippenstiel, Louis Scharf, and Douglas Williams, who reviewed a former version
of
the
book and provided
us
with numerous useful comments and suggestions.
It
was a pleasure
to
work
with the excellent staff at Prentice Hall, and we are particularly appreciative
of
Tom Robbins and
Scott Disanno for their professional expertise.
Many
of
the topics described in this book are outgrowths
of
our research programs in statistical
signal and array processing, and we wish to thank the sponsors
of
this research: the Swedish
Foundation for Strategic Research, the Swedish Research Council, the Swedish Institute, the
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