通信系统第一章翻译

如果观测随机过程 X(t)（从 t=-∞开始）所得到的每一组随 机变量的联合分布函数对于 不同的时间原点 t=0 是时不 变的，那么随机过程 X(t)是严 平稳的。
jointly strictly stationary The first-order distribution of a stationary random process is independent of time.
sample point
采样点
sample space
采样空间
random or stochastic process
随机过程
total observation interval
总观测区间
realization
实现
sample function
样本函数
random variable
随机变量
We may now formally define a
autocorrelation function
ergodic in the autocorrelation
自相关函数遍历
function
1.6 Transmission of a Random Process Through a Linear Time-Invariant Filter
随机过程通过一个线性时不变滤波器
process multiplied by the
squared magnitude response
of the filter
Einstein-Wiener-Khintchine Einstein-Wiener-Khintchine 关
relations
系式
The zero-frequency value of
平稳过程功率谱密度的零频
the power spectral density of
率值等于自相关函数曲线下
a stationary process equals
的全部面积
the total area under the graph of the autocorrelation function The mean-square value of a stationary process equals the total area under the graph of the power spectral density The power spectral density of a stationary process is always nonnegative The power spectral density of a real-valued random process is an even function of frequency The power spectral density, appropriately normalized, has the properties usually associated with a probability density function
weakly stationary process.
严格平稳随机过程的自相关
函数只与时间差 t1 − t2 有关。
二维平稳过程、宽平稳过程 和弱平稳过程。
mean-square value decorrelation time uniformly distributed
binary symbols
均方根值 去相关时间 均匀分布 二进制符号
times
1.4 Mean，Correlation，and Covariance Functions
均值、相关函数和协方差函数
mean
均值
The mean of a strictly
严平稳随机过程的均值是一
stationary process is a
个常量。
constant
autocorrelation function
1.3 Stationary Processes 平稳过程 平稳的 不平稳
严格意义上的平稳或者严平 稳
a random process X(t), initiated at time t=-∞,is strictly stationary if the joint distribution of any set of random variables obtained by observing the random process X(t) is invariant with respect to the location of the origin t=0.
现在，可以正式的定义一个
random process X(t) as an
随机过程 X（t）为具有一定
ensemble of time functions
概率规则的时间函数的集
together with a probability
合，这个概率规则就是为任
rule that assigns a probability
自相关函数
the autocorrelation function of a strictly stationary process depends only on the time
difference t1 − t2
second-order
stationary,
wide-sense stationary, or
的平方值等于输入的功率谱
filter in response to a
密度与滤波器幅度响应平方
stationary process is equal to
的乘积在整个频域上的积分
the integral over all
frequencies of the power
spectral density of the input
What happens to a stationary random process when it is transmitted through a linear time-invariant filter?
平稳随机过程具有遍历性必 须满足的条件，这为采用集 平均代替时间平均提供了可 能。
当一个平稳随机过程通过一 个线性时不变滤波器时会发 生的变化。
幅度响应
power spectral density or
功率谱密度 或
power spectrum
功率谱
the mean-square value of the
一个稳定的线性时不变系统
output of the output of a
对一个平稳过程的响应输出
stable linear time-invariant
何与随机过程的一个样本函
to any meaningful event
数观察值有关的有意义事件
associated
with
an
都分配一定的概率。
observation of one of the
sample functions of the
random process.
stationary nonstationary stationary in the strict sense or strictly stationary
1.1 Introduction 简介
数学模型 确定的 可能性 随机的
信载信号
interference component channel noise thermal noise
干扰成分 信道噪声
热噪声
1.2 Mathematical Definition of a Random Process
随机过程的数学定义
数学期望 或
ensemble averages
集平均
long-term sample averages
长期样本平均 或
or
时间平均
time averages
estimation
估计
unbiased estimate
无偏估计
ergodic in the mean
均值遍历
time-averaged
时间平均自相关函数
Sources of noise and their narrowband form.
采用功率谱密度对随机过程 进行频域描述。
重要的一种随机过程：高斯 过程的特性。
噪声源及其窄带形式。
Rayleigh and Rician distributions, which represent
瑞利分布和莱斯分布是通信 系统研究中产生的两类重要
two special probability distributions that arise in the study of communication systems.
的概率分布。
mathematical model deterministic probability
stochastic or random information-bearing signal
The conditions that have to be satisfied for a stationary random process to be ergodic, a property that enables us to substitute time averages for ensemble averages.
linear time-invariant filter of 冲激响应 h(t)的线性时不变
impulse response h(t)
滤波器
convolution integral
卷积积分
1.7 Power Spectral Density
功率谱密度
frequency response
频率响应
magnitude response
联合严平稳
平稳函数的一维分布函数与 时间无关。
The second-order distribution
平稳过程的二维分布函数只
function of a stationary
与观测的时间差有关
Leabharlann Baidu
random process depends only
on the time difference
between the observation
conditional expectation cross-correlation functions
条件期望 互相关函数
correlation matrix
相关矩阵
quadrature-modulated
正交调制过程
processes
1.5 Ergodic Processes
遍历过程
expectations or
Chapter 1 Random Processes
第一章 随机过程
英文斜体部分
词语翻译
句子翻译
The notion of a random
随机过程的概念。
process.
The requirement that has to
一个随机过程是平稳随机过
be satisfied for a random
程必须满足的条件。
process to be stationary.
The partial description of a random process in terms of its mean,correlation,and covariance functions.
对随机过程的均值、相关函 数、以及协方差函数的分别 描述。
The
frequency-domain
description of a random
process in terms of power
spectral density.
The characteristics of an important type of random process known as a Gaussian process.
delta function energy spectral density symbol shaping pulse
symbol duration
mixing
the power spectral density of the output process Y(t) equals the power spectral density of
the input process X(t) multiplied by the squared magnitude response of the
filter. power signal
periodogram estimating
delta 函数 能量谱密度 符号整形脉冲 符号持续时间