数字信号处理英文文献及翻译

数字信号处理

一、导论

数字信号处理（DSP）是由一系列的数字或符号来表示这些信号的处理的过程的。数字信号处理与模拟信号处理属于信号处理领域。DSP包括子域的音频和语音信号处理，雷达和声纳信号处理，传感器阵列处理，谱估计，统计信号处理，数字图像处理，通信信号处理，生物医学信号处理，地震数据处理等。

由于DSP的目标通常是对连续的真实世界的模拟信号进行测量或滤波，第一步通常是通过使用一个模拟到数字的转换器将信号从模拟信号转化到数字信号。通常，所需的输出信号却是一个模拟输出信号，因此这就需要一个数字到模拟的转换器。即使这个过程比模拟处理更复杂的和而且具有离散值，由于数字信号处理的错误检测和校正不易受噪声影响，它的稳定性使得它优于许多模拟信号处理的应用（虽然不是全部）。

DSP算法一直是运行在标准的计算机，被称为数字信号处理器（DSP）的专用处理器或在专用硬件如特殊应用集成电路（ASIC）。目前有用于数字信号处理的附加技术包括更强大的通用微处理器，现场可编程门阵列（FPGA），数字信号控制器（大多为工业应用，如电机控制）和流处理器和其他相关技术。

在数字信号处理过程中，工程师通常研究数字信号的以下领域：时间域（一维信号），空间域（多维信号），频率域，域和小波域的自相关。他们选择在哪个领域过程中的一个信号，做一个明智的猜测（或通过尝试不同的可能性）作为该域的最佳代表的信号的本质特征。从测量装置对样品序列产生一个时间或空间域表示，而离散傅立叶变换产生的频谱的频率域信息。自相关的定义是互相关的信号本身在不同时间间隔的时间或空间的相关情况。

二、信号采样

随着计算机的应用越来越多地使用，数字信号处理的需要也增加了。为了在计算机上使用一个模拟信号的计算机，它上面必须使用模拟到数字的转换器（ADC）使其数字化。采样通常分两阶段进行，离散化和量化。在离散化阶段，信号的空间被划分成等价类和量化是通过一组有限的具有代表性的信号值来代替信号近似值。

奈奎斯特-香农采样定理指出，如果样本的取样频率大于两倍的信号的最高频率，一个信号可以准确地重建它的样本。在实践中，采样频率往往大大超过所需的带宽的两倍。

数字模拟转换器（DAC）用于将数字信号转化到模拟信号。数字计算机的使用是数字控制系统中的一个关键因素。

三、时间域和空间域

在时间或空间域中最常见的处理方法是对输入信号进行一种称为滤波的操作。滤波通常包括对一些周边样本的输入或输出信号电流采样进行一些改造。现在有各种不同的方法来表征的滤波器，例如：

一个线性滤波器的输入样本的线性变换；其他的过滤器都是“非线性”。线性滤波器满足叠加条件，即如果一个输入不同的信号的加权线性组合，输出的是一个同样加权线性组合所对应的输出信号。

“因果”滤波器只使用以前的样本的输入或输出信号；而“非因果”滤波器使用未来的输入样本。一个非因果滤波器通常可以通过增加一个延迟将它变成了一个因果滤波器。

“时间不变”滤波器随着时间的推移性具有稳定特性；其他滤波器如随时间变化的自适应滤波器。

一些滤波器是“稳定”的，别的是“不稳定的”。一个稳定的滤波器产生的输出信号随时间收敛于一个恒定值，或在一个有限的时间间隔内是有界的。一种不稳定的滤波器可以产生一个没有增长界限的输出，甚至零输入有界。

“有限脉冲响应（FIR）”滤波器只使用于输入信号，而“无限脉冲响应滤波器（IIR）”使用于输入信号和输出信号之前的样品。FIR滤波器总是稳定的，而IIR滤波器可能是不稳定的。

大多数滤波器可以被描述在z域（频域的一个超集）的传递函数。如果它是一个FIR滤波器的脉冲响应和阶跃响应，滤波器也可以被描述为一个差分方程，或对零点和极点的收集。一个FIR滤波器的输出是通过对任何给定的输入与脉冲响应的卷积计算得到的。滤波器也可以被用来推导出一个样品的处理算法的方块图利用硬件指令实现滤波器所代表。

四、频域

信号通常是通过傅立叶变换将其从时间或空间域转换到频率域。傅里叶变换将信号转换信息和相位分量级的每个频率。通常的傅里叶变换转换为功率谱，这是大小的每个频率分量的平方。

在频域对信号分析的最常见的用途是信号特性分析。工程师可以研究频谱来确定哪一频率的存在于输入信号中。

滤波，特别是在非实时的工作也可以被转换到频域实现，应用滤波器，然后转换回时域。这是一个快速，O（nlogn）操作，可以基本上给出任何滤波器的形状包括砖墙滤波器优良的逼近。

有一些常用的频域变换。例如，倒谱转换信号的频域傅立叶变换，取对数，然后将另一个傅里叶变换。这强调的频率成分的幅度较小而保留的频率分量的大小顺序。频域分析又称谱或谱分析。

五、信号处理

信号通常需要以不同的方式进行处理。例如，从一个传感器的输出信号可能被污染的多余电“噪音”。电极连接到一个病人的胸部时，心电图是测量由心脏和其他肌肉的活动引起的微小的电压变化。由于电的干扰从电源的强烈影响，信号通常是采用“总管拾取”。处理信号的滤波电路可以消除或至少降低信号的不需要的部分。现在，越来越多的的情况下，是由DSP技术来进行信号的滤波以提高信号质量或提取重要信息，而不是模拟电子技术。

六、DSP的发展

数字信号处理的发展从1960年代的大型数字计算机的数字运算应用程序的使用快速傅立叶变换（FFT），它允许一个信号的频谱可以快速计算。这些技术在当时没有被广泛使用，因为合适的计算设备通常仅在大学及其他科研机构可以使用。

七、数字信号处理器（DSP）

在20世纪70年代末和20世纪80年代初微处理机的介绍使DSP技术在更广泛的范围内得到了使用。然而，通用微处理器如Intel x86的家庭并不适合于DSP的计算密集型的需求，随着20世纪80年代DSP重要性的增加导致几个主要的电子产品制造商（如德克萨斯仪器，模拟设备和摩托罗拉）去开发数字信号处理器芯片，专门的微处理器，专门设计用于在数字信号处理要求的操作的类型的架构。（注意，缩写DSP数字信号处理的不同的意思，这个词用于处理数字信号，多种技术或数字信号处理器，一种特殊类型的微处理器芯片）。像一个通用微处理器，DSP是一种具有其自己的本地指令代码的可编程器件。DSP芯片是能够每秒进行数以百万计的浮点运算，像他们同类型的更著名的通用器件，更快和更强大的版本正在不断被引入。DSP也可以嵌入在复杂的“系统芯片”装置，通常包括模拟和数字电路。

8、数字信号处理器的应用

DSP技术是当今普遍在手机，多媒体计算机，录像机，CD播放器，硬盘驱动器和控制器的调制解调器等设备，并将很快在电视和电话业务中取代模拟电路。DSP的一个重要的应用是信号的压缩和解压。信号压缩用于数字蜂窝电话，在每一个地方的“单元”让更多的电话同时被处理。DSP信号压缩技术不仅使人们可以相互交谈，而且可以通过使用安装在计算机上的小的摄像机使人们通过显示器看见对方，而这些只需要将传统的电话线连接在一起。在音频CD 系统，DSP技术来执行复杂的错误检测和校正原始数据，因为它是从光盘读取。

虽然一些潜在的DSP技术的数学理论，如傅立叶和希尔伯特变换，数字滤波器的设计和信号压缩，可以相当复杂，而数值运算所需的实际实现这些技术是非常简单的，主要包括操作可以在一个便宜的四功能的计算器上进行操作。一种DSP芯片的结构设计进行这样的操作非常快，处理的样品每秒数以亿计，提供实时的性能：即，能够处理一个实时的信号，因为它是采样，然后输出信号的处理，例如扬声器或视频显示。所有的DSP应用前面提到的实例，如硬盘驱动器和移动电话，要求实时操作。

主要电子产品制造商已投入巨资在DSP技术。因为他们现在发现在大众市场的产品应用中，DSP芯片的电子装置占有世界市场的很大比例。销售额每年数十亿美元，并可能继续快速增长。

DSP主要应用的音频信号处理，音频压缩，数字图像处理，视频压缩，语音处理，语音识别，数字通信，雷达，声纳，地震，和生物医学。具体的例子是在数字移动电话的语音压缩与传输，空间匹配均衡的音响、扩声领域，良好的天气预测，经济预测，地震数据处理，和工业过程控制分析，计算机生成的动画电影中，医学影像如CAT扫描和MRI，MP3压缩，图像处理，高保真度扬声器分频器和均衡，并与电吉他放大器使用的音频效果。

九、数字信号处理的实验

数字信号处理是经常使用专门的微处理器，如dsp56000，TMS320，或SHARC。这些通常处理数据使用定点运算，虽然某些版本可以使用浮点算法和更强大。更快的应用FPGA可能从慢启动流处理器应用Freescale公司的出现，传统的较慢的处理器如单片机可能是适当的。

【英文原文】

Digital Signal Processing

1、Introduction

Digital signal processing (DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, biomedical signal processing, seismic data processing, etc.

Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another analog output signal, which requires a digital to analog converter. Even if this process is more complex than analog processing and has a discrete value range, the stability of digital signal processing thanks to error detection and correction and being less vulnerable to noise makes it advantageous over analog signal processing for many, though not all, applications.

DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSP)s, or on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors, among others.

In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.

2、Signal Sampling

With the increasing use of computers the usage of and need for digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replace the signal with representative signal values are approximated by values from a finite set.

The Nyquist-Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the samples if the sampling frequency is greater than twice the highest frequency of the signal. In practice, the sampling frequency is often significantly more than twice the required bandwidth.

A digital to analog converter (DAC) is used to convert the digital signal back to analog signal. The use of a digital computer is a key ingredient in digital control systems.

3 、Time and Space Domains

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters, for example: A “linear” filter is a linear transformation of input samples; other filters are “non-linear.” Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.

A “causal”filter uses only previous samples of the input or output signals; while a “non-causal” filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.

A “time-invariant”filter has constant properties over time; other filters such as adaptive filters change in time.

Some filters are “stable”, others are “unstable”. A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An converges to a constant value with time, or remains bounded within a finite interval. An unstable filter can produce an output that grows without bounds, with bounded or even zero input.

A “Finite Impulse Response”(FIR) filter uses only the input signal, while an “Infinite Impulse Response” filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.

Most filters can be described in Z-domain (a superset of the frequency domain) by their transfer functions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response. The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. Filters can also be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions.

4、Frequency Domain

Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.

The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing.

Filtering, particularly in non real-time work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O (n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filters.

There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components. Frequency domain

analysis is also called spectrum or spectral analysis.

5、Signal Processing

Signals commonly need to be processed in a variety of ways. For example, the output signal from a transducer may well be contaminated with unwanted electrical “noise”. The electrodes attached to a patient’s chest when an ECG is taken measure tiny electrical voltage changes due to the activity of the heart and other muscles. The signal is often strongly affected by “mains pickup” due to electrical interference from the mains supply. Processing the signal using a filter circuit can remove or at least reduce the unwanted part of the signal. Increasingly nowadays, the filtering of signals to improve signal quality or to extract important information is done by DSP techniques rather than by analog electronics.

6、Development of DSP

The development of digital signal processing dates from the 1960’s with the use of mainframe digital computers number-crunching applications such an the Fast Fourier Transform (FFT), which allows the frequency spectrum of a signal to be computed rapidly. These techniques are not widely used at that time, because suitable computing equipment was generally available only in universities and other scientific research institutions.

7、Digital Signal Processors (DSPs)

The introduction of the microprocessor in the late 1970’s and early 1980’s made it possible for DSP techniques to be used in a much wider range of applications. However, general-purpose microprocessors such as the Inter x86 family are not ideally suited to the numerically-intensive requirements of DSP, and during the 1980’s the increasing importance of DSP led several major electronics manufacturers (such as Texas Instruments, Analog Devices and Motorola) to develop Digital Signal Processor chips-specialised microprocessors with architectures designed specifically for the types of operations required in digital signal processing.(Note that the acronym DSP can variously mean Digital Signal Processing, the term used for a wide range of techniques for processing signals digitally, or Digital Signal Processor, a specialized type of microprocessor chip). Like a general-purpose microprocessor, a DSP is a programmable device, with its own native instruction code. DSP chip are capable of carrying out millions of floating point operations per second, and like their better-known general-purpose cousins, faster and more powerful versions are continually being introduced. DSPs can also be embedded within complex “system-on-chip” devices, often containing both analog and digital circuitry.

8、Applications of DSP

DSP technology is nowadays commonplace in such devices as mobile phones, multimedia computers, video recorders, CD players, hard disc drive controllers and modems, and will soon replace analog circuitry in TV sets and telephones. An important application of DSP is in signal compression and decompression. Signal compression is used in digital cellular phones to allow a greater number of calls to be handled simultaneously within each local “cell”. DSP signal compression technology allows people not only to talk to one another but also to see one anther on their computer screens, using small video cameras mounted on the computer monitors, with only a conventional telephone line linking them together. In audio CD systems, DSP technology is used to perform complex error detection and correction on the raw data as it is read from the CD.

Although some of the mathematical theory underlying DSP techniques, such as Fourier and Hilbert transforms, digital filter design and signal compression, can be fairly complex, the numerical operations required actually to implement these techniques are very simple, consisting

mainly of operations that could be done on a cheap four-function calculator. The architecture of a DSP chip is designed to carry out such operations incredibly fast, processing hundreds of millions of samples every second, to provided real-time performance: that is , the ability to process a signal “live” as it is sampled and then output the processed signal, for example to a loudspeaker or video display. All of the practical examples of DSP applications mentioned earlier, such as hard disc drives and mobile phones, demand real-time operation.

The major electronics manufacturers have invested heavily in DSP technology. Because they now find application in mass-market products, DSP chips account for a substantial proportion of the world market for electronic devices. Sales amount to billions of dollars annually, and seem likely to continue to increase rapidly.

The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology, and biomedicine. Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in hi-fi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, MP3 compression, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers.

9、Implementation

Digital signal processing is often implemented using specialized microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixed-point arithmetic, although some versions are available which use floating point arithmetic and are more powerful. For faster applications FPGAs might be emerge from companies including Freescale and startup Stream Processors Inc. For slow applications, a traditional slower processor such as a microcontroller may be adequate.