掌握数字信号处理：MATLAB实践指南

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"《Digital Signal Processing Using MATLAB for Students and Researchers》是一本面向学生和研究人员的数字信号处理教材，强调实践应用和算法技术，旨在帮助读者理解数字信号处理的基本原理，并将其应用于数字电视、移动通信、宽带通信以及医疗/科学设备等实际领域。作者是John W. Leis，来自澳大利亚南昆士兰大学。本书由John Wiley & Sons, Inc. 出版，并同时在加拿大发行。" 在数字信号处理领域，MATLAB是一种广泛使用的工具，因其强大的计算能力和友好的用户界面而深受青睐。本书通过MATLAB平台，深入浅出地介绍了数字信号处理的核心概念和技术。首先，它涵盖了数字信号的基础知识，如离散时间信号与系统、傅立叶变换以及数字滤波器的设计。这些基础知识对于理解和应用数字信号处理至关重要。在讲解过程中，作者采用实践导向的方法，鼓励读者动手操作MATLAB，通过编写代码来解决实际的信号处理问题。例如，书中可能包含如何使用MATLAB进行信号采样、量化、谱分析以及噪声抑制等内容。这样的实践环节不仅有助于巩固理论知识，也能提高读者的实际操作技能。此外，书中还可能探讨了更高级的主题，如快速傅立叶变换(FFT)、小波分析、自适应滤波器和数字信号处理器(DSP)系统设计。这些内容对于深入理解信号处理在通信、图像处理和音频处理等领域的应用至关重要。书中可能还包含了各种实例和项目，以帮助读者将所学知识应用于实际问题，如通信系统的误码率计算、医学图像的去噪处理或者音频信号的压缩。这些实例可能来自于不同的工程和科研背景，使学习更具针对性和实用性。《Digital Signal Processing Using MATLAB for Students and Researchers》是一本实用的教程，它通过MATLAB这一强大工具，为学生和研究人员提供了学习和掌握数字信号处理理论与实践的宝贵资源。无论是初学者还是有一定基础的读者，都能从中受益，提升自己在信号处理领域的专业能力。

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1.5 APPLICATION CASE STUDIES USING DSP 7

required sampling rate (in this example, 96,000 samples per second). Figure 1.3

shows the resulting measurements, with the microphone placed at various distances

from the speaker. What is immediately clear is that the amplitude of the received

signal decreases with the distance, as would be expected. Furthermore, the relative

delay or phase of the tone changes according to the distance. This change could be

used to estimate the distance of the microphone from the speaker. One complication

is that the signal clearly contains some additional noise, which must be reduced in

order to make a more accurate measurement.

The estimates derived from Figure 1.3 yield a ﬁ gure of 12 - cm movement for

the case where the microphone was moved from 5 to 15 cm, and an estimate of 18 cm

for the 5 - to 25 - cm microphone movement. What factors inﬂ uence the accuracy of

the result? Clearly, we must make an assumption for the speed of sound, but in

addition, we need to determine the relative phase of the sinusoids as accurately as

possible. Correlation algorithms (mentioned earlier) are of some help here. It also

helps to maximize the sampling rate since a higher rate of sampling means that the

sound travels a shorter distance between samples.

Other information about the speaker – microphone – room coupling can be

gleaned by using a different test signal, which is not difﬁ cult to do using DSP tech-

niques. Figure 1.4 shows the result of using random noise for the output signal (the

random noise is also termed “ white noise ” by analogy with white light, which com-

prises all wavelengths). This type of signal is a broad - spectrum one, with no one

FIGURE 1.3 The response of the speaker – microphone system to a pure tone, with the

microphone placed at various distances away from the source. The relative delay may be

used to estimate distance. Note that the signals, particularly those at larger distances, have

a larger component of noise contamination.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

−2,000

−1,500

−1,000

−500

500

1,000

1,500

2,000

Time (ms)

Sample value

25 cm

15 cm

5 cm

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8 CHAPTER 1 WHAT IS SIGNAL PROCESSING?

pure tone dominating over any other. The ﬁ gure shows the energy content over the

frequency range of the output signal and the estimated energy content over the same

range of frequencies as received by the microphone. This is a derived result in that

all that is available directly are the sample values at each sampling instant, and it is

necessary to derive the corresponding frequency components indirectly. The algo-

rithms for performing this analysis are introduced in Chapter 7 . From Figure 1.4 it

is evident that the speaker – microphone channel exhibits what is termed a “ bandpass ”

characteristic — lower frequencies are reduced in amplitude (attenuated), and higher

frequencies are also reduced substantially. This information may be used to com-

pensate for the shortcomings of a particular set of conditions — for example, boosting

frequencies which have been reduced so as to compensate for the acoustics and

speaker setup.

Figure 1.5 shows a different set of results as calculated from the broad -

spectrum experiment. Here, we perform a system identiﬁ cation algorithm using the

correlation function (as discussed in Chapter 6 ) at each of the microphone displace-

ments. Each response has been normalized to a ± 1 amplitude level for easier com-

parison. It is clear that the displacement of each waveform corresponds to the time

delay, as discussed. However, the shape of the graphs is approximately the same.

This characteristic response shape is termed the impulse response . This is a key

concept in signal processing — the impulse response is that response produced by a

system (in this case, the electroacoustic system) as a result of a single pulse. In most

FIGURE 1.4 The estimated frequency response of the audio system. This particular

system clearly shows a marked reduction in the transmission of higher - frequency audio

components.

0 6 12 18 24

−30

−20

−10

Frequency (kHz)

Power (dB)

Output power spectrum

0 6 12 18 24

−30

−20

−10

Frequency (kHz)

Power (dB)

Input power spectrum

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1.5 APPLICATION CASE STUDIES USING DSP 11

FIGURE 1.7 The relative value of the frequency - ﬁ ltered root mean square energy

derived for each image. This is seen to correspond to the relative focus of each image. In

this case, we need to apply several DSP algorithms to the image data to synthesize one

parameter which is representative of the quantity we desire, the degree of focus. The

asterisk (*) indicates the energy in the camera ’ s auto - focused image.

0 5 10 15 20 25 30 35 40

RMS energy of high-pass filtered image

Image number

Autofocus

with an unprecedented view inside the human body from external noninvasive scan-

ning measurements.

The fundamental idea of tomography is to take many projections through an

object and to construct a visualization of the internals of the object using post-

processing algorithms. Figure 1.8 shows a schematic of the setup of this arrange-

ment. The source plane consists of X - ray or other electromagnetic radiations

appropriate to the situation. A series of line projections are taken through the object,

and the measurements at the other side are collated as illustrated by the graph in the

ﬁ gure . This gives only one plane through the object — a cross - sectional view only.

What we desire is a two - dimensional view of the contents of the object. In a math-

ematical sense, this means a value of f ( x , y ) at every ( x , y ) point in a plane. A single

cross - sectional slice does not give us an internal view, only the cross - sectional

projection.

The key to the visualization is to take multiple cross sections, as illustrated in

Figure 1.9 . This shows two cross sections of the object, each at an angle θ from

the x axis. The projection of a particular point, as illustrated in the ﬁ gure, yields the

equivalent density at the point ( x , y ) inside the object, shown as the dot where the

two ray traces intersect. The ﬁ gure shows only two projections; in reality, we need

to take multiple projections around the object in order to resolve all ambiguities in

the value of the intensity f ( x , y ).

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