信号处理入门：理论与实践

需积分: 10 116 浏览量更新于2024-07-23 1 收藏 6.87MB PDF 举报

《信号处理入门》是Sophocles J. Orfanidis教授编著的一本关于信号处理领域的教材，适用于那些希望深入理解信号处理基本原理和技术的读者。这本书是基于Rutgers University的课程，并且曾由Pearson Education, Inc. 和 Prentice Hall, Inc. 出版。版权信息显示，未经作者Sophocles J. Orfanidis的书面许可，不得以任何形式复制、存储或传输本书的部分内容。该书的第一章“采样与重建”是全书的起点，主要涵盖了以下几个关键知识点： 1. **章节介绍**：首先引导读者对信号处理领域进行概述，明确其在信息技术中的核心地位和应用范围。 2. **模拟信号回顾**：这部分简要回顾了模拟信号的基本概念，强调它们在现实世界中的物理表示形式，如连续时间和幅度特性。 3. **采样定理**：这是信号处理的基础，它阐述了如何将连续时间信号转换为离散时间信号。采样定理指出，为了不失真地恢复原始信号，必须确保采样频率至少是信号最高频率的两倍（即奈奎斯特频率）。 - **采样定理示例**：通过具体例子如正弦波的采样，解释了如果采样频率不足，可能导致信号失真（即混叠效应）。 4. **抗混叠滤波器**：针对采样过程中可能出现的混叠问题，介绍了抗混叠滤波器的作用，它们在实际系统中用于减少或消除混叠失真。 5. **硬件限制**：讨论了实际硬件在采样过程中的局限性，包括噪声、功耗和速度等因素，这些都是工程师在设计信号处理系统时需要考虑的因素。 6. **采样正弦波的细节**：深入探讨了如何采样正弦波，以及如何通过适当的滤波和数字信号处理技术来实现无失真重建。 7. **旋转运动中的信号处理**：展示了信号处理在工程中的实际应用，如机械系统中的角频率处理，以及如何将这些概念扩展到更复杂的动态场景。 8. **数字频率单位**：介绍了数字信号处理中的特定频率单位，例如离散频率（Hz），这对于理解和解析采样信号的频域特性至关重要。《信号处理入门》以采样理论为核心，逐步介绍了信号从模拟到数字的转换过程，以及在实际应用中如何处理和分析这些数字化信号。通过阅读这本书，读者可以建立起坚实的信号处理基础，为后续的深入学习和实践打下坚实的基础。

4 1. SAMPLING AND RECONSTRUCTION

The input spectrum

X(Ω) consists of two sharp spectral lines at frequencies Ω

and

, as can be seen by taking the Fourier transform of x(t):

X(Ω)= 2πA

δ(Ω − Ω

)+2πA

δ(Ω − Ω

)

The corresponding output spectrum Y(Ω) is obtained from Eq. (1.2.4):

Y(Ω) = H(Ω)X(Ω)= H(Ω)



2πA

δ(Ω − Ω

)+2πA

δ(Ω − Ω

)



2πA

H(Ω

)δ(Ω − Ω

)+2πA

H(Ω

)δ(Ω − Ω

)

What makes the subject of linear ﬁltering useful is that the designer has complete

control over the shape of the frequency response

H(Ω) of the ﬁlter. For example, if the

sinusoidal component

represents a desired signal and Ω

an unwanted interference,

then a ﬁlter may be designed that lets

pass through, while at the same time it ﬁlters

out the

component. Such a ﬁlter must have H(Ω

)= 1 and H(Ω

)= 0.

1.3 Sampling Theorem

Next, we study the sampling process, illustrated in Fig. 1.3.1, where the analog signal

x(t) is periodically measured every T seconds. Thus, time is discretized in units of the

sampling interval

t = nT, n = 0, 1, 2,...

Considering the resulting stream of samples as an analog signal, we observe that

the sampling process represents a very drastic chopping operation on the original signal

x(t), and therefore, it will introduce a lot of spurious high-frequency components into

the frequency spectrum. Thus, for system design purposes, two questions must be

answered:

1. What is the effect of sampling on the original frequency spectrum?

2. How should one choose the sampling interval

We will try to answer these questions intuitively, and then more formally using

Fourier transforms. We will see that although the sampling process generates high

frequency components, these components appear in a very regular fashion, that is, ev-

ery frequency component of the original signal is periodically replicated over the entire

frequency axis, with period given by the sampling rate:

(1.3.1)

This replication property will be justiﬁed ﬁrst for simple sinusoidal signals and then

for arbitrary signals. Consider, for example, a single sinusoid

x(t)= e

2πjf t

of frequency

f. Before sampling, its spectrum consists of a single sharp spectral line at f. But after

sampling, the spectrum of the sampled sinusoid

x(nT)= e

2πjf nT

will be the periodic

replication of the original spectral line at intervals of

, as shown in Fig. 1.3.2.

8 1. SAMPLING AND RECONSTRUCTION

Example 1.3.2:

Similarly, the spectrum of speech preﬁltered to about 4 kHz results in very

intelligible speech. Therefore, in digital speech applications it is adequate to use sampling

rates of about 8 kHz and preﬁlter the speech waveform to about 4 kHz.



What happens if we do not sample in accordance with the sampling theorem? If we

undersample, we may be missing important time variations between sampling instants

and may arrive at the erroneous conclusion that the samples represent a signal which

is smoother than it actually is. In other words, we will be confusing the true frequency

content of the signal with a lower frequency content. Such confusion of signals is called

aliasing and is depicted in Fig. 1.3.6.

true signal

2T 3T 4T 5T 6T

8T 9T 10T

aliased signal

Fig. 1.3.6 Aliasing in the time domain.

1.3.3 Hardware Limits

Next, we consider the restrictions imposed on the choice of the sampling rate f

by the

hardware. The sampling theorem provides a lower bound on the allowed values of

The hardware used in the application imposes an upper bound.

In real-time applications, each input sample must be acquired, quantized, and pro-

cessed by the DSP, and the output sample converted back into analog format. Many

of these operations can be pipelined to reduce the total processing time. For example,

as the DSP is processing the present sample, the D/A may be converting the previous

output sample, while the A/D may be acquiring the next input sample.

In any case, there is a total processing or computation time, say

proc

seconds, re-

quired for each sample. The time interval

T between input samples must be greater

than

proc

; otherwise, the processor would not be able to keep up with the incoming

samples. Thus,

T ≥ T

proc

or, expressed in terms of the computation or processing rate, f

proc

= 1/T

proc

, we obtain

the upper bound

≤ f

proc

, which combined with Eq. (1.3.2) restricts the choice of f

the range:

max

≤ f

proc

In succeeding sections we will discuss the phenomenon of aliasing in more detail,

provide a quantitative proof of the sampling theorem, discuss the spectrum replication

剩余794页未读，继续阅读

qq_20518093

粉丝: 0
资源: 2

信号处理入门：理论与实践

Introduction To signal Processing--Sophocles J.Orfanidis信号处理导论

Introduction to Sound Processing

Intro To Signal Processing

intro to java资源

intro 重写intro下一步方法

Intro to MapView - Create a 2D map - 4.5创建2D地图并实现简单功能代码

引用intro.js文件生成网页前端代码

angular intro.js 使用

angular intro.js

在mobile后面添加“intro+学号” 字段；

最新资源