数字信号处理翻译

吴楠电子与通信工程2014309013 Signal processing

Signal processing is an area of electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time, to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signalling are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

History

According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the "digitalization" or digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.[2]

Categories of signal processing

Analog signal processing

Analog signal processing is for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and

phase-locked loops.

Discrete time signal processing

Discrete time signal processing is for sampled signals that are considered as defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.

The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.

Digital signal processing

Digital signal processing is for signals that have been digitized. Processing is done by general-purpose computers or by digital circuits such as ASICs,

field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and look-up tables. Examples of algorithms are the Fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters

1.Digital signal processing

Digital signal processing (DSP) is concerned with the representation of 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, control of systems, biomedical signal processing, seismic data processing, etc.

The goal of DSP is usually to measure, filter and/or compress continuous

real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling it using an analog-to-digital converter (ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a

digital-to-analog converter (DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.[1]

DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors (DSPs), 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 apps such as motor control), and stream processors, among others.[2]

2. DSP domains

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.

3. Signal sampling

Main article: Sampling (signal processing)

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. 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 replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the 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 sampling frequency is greater than twice the highest frequency of the signal; but requires an infinite number of samples . In practice, the sampling frequency is often significantly more than twice that required by the signal's limited bandwidth.

A digital-to-analog converter is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient in digital control systems. 4. Time and space domains

Main article: Time domain

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear 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 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 signals, 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.

Filters can be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. 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 a digital filter to any given input may be calculated by convolving the input signal with the impulse response.

5. Frequency domain

Main article: 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.

In addition to frequency information, phase information is often needed. This can be obtained from the Fourier transform. With some applications, how the phase varies with frequency can be a significant consideration.

Filtering, particularly in non-realtime 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 through 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.

6. Z-domain analysis

Whereas analog filters are usually analysed on the s-plane; digital filters are analysed on the z-plane or z-domain in terms of z-transforms.

Most filters can be described in Z-domain (a complex number superset of the frequency domain) by their transfer functions. A filter may be analysed in the z-domain by its characteristic collection of zeroes and poles.

7. Applications

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 Hifi 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

8. Implementation

Digital signal processing is often implemented using specialised 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[3] might be used. Beginning in 2007, multicore

implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also a growing number of DSP applications are now being implemented on Embedded Systems using powerful PCs with a Multi-core processor.

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信号处理

信号处理是电子工程与应用数学领域，在离散时间或者连续时间域处理和分析信号，来对这些信号进行所需的必要的处理。这些信号包括语音、图像、时变测量值与传感器的数据,例如生物资料如心电图、控制系统信号,电信传递讯号如无线电信号,以及其他许多种形式。模拟或数字信号代表空间变换或者时变的物理量。在信号处理中，任意二进制数据流、开关信号没有被作为实质的信号，而是被当做代表模拟物理量的模拟和数字信号。

发展历史

根据Alan V. Oppenheim和Ronald W. Schafer的研究，信号处理可以在十七世纪的经典数据分析中被发现。他们进一步研究表明这种技术的数字化和数字精度在二十世纪的四十年代到五十年代的数控领域都得到了应用。

信号处理的类别

模拟信号处理

模拟信号处理是针对那些没有被数字化的信号所做的处理，例如在老式的电台、电话、雷达和电视系统中的信号。这包括线性电路,如无源滤波器、有源滤波器、累加器、集成商和延迟线。同时也涉及到非线性电路,如(混频器、压控放大器、压控过滤器、压控振荡器、锁相环等。

离散时间信号处理

离散时间信号处理是针对在离散时间点上采样的信号，但它们只是时间上离散，而在幅度上并不离散。模拟离散时间信号处理，如采样和保持电路，模拟时分多路复用器，模拟延迟线和模拟反馈移位寄存器的电子装置为基础的技术。这项技术是一种数字信号处理（见下文）的前身，至今依然是在千兆赫信号先进的加工使用。在离散时间信号处理概念也指的是一个理论学科，它建立了数字信号处理的数学基础，而不考虑量化误差。

数字信号处理

数字信号处理是已经数字化的信号。加工是由通用计算机或专用集成电路等，现场可编程门阵列或专门的数字信号处理器（DSP芯片）数字电路。典型的算术运算包括定点和浮点，实数和复数，乘法和加法。由硬件支持的其他典型的操作循环缓冲器和查找表。对算法的例子是快速傅立叶变换（FFT），有限脉冲响应（FIR）滤波器，无限脉冲响应（IIR）滤波器，以及诸如维纳和卡尔曼滤波自适应滤波器。

1.数字信号处理

数字信号处理（DSP）是关注的信号通过一组数字或符号序列，这些信号处理的代表性。数字信号处理和模拟信号处理是信号处理的子领域。DSP的包括像子字段：音频和语音信号处理，声纳和雷达信号处理，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，系统控制，生物医学信号处理，地震数据处理。

DSP的目标通常衡量，筛选器和/或压缩连续现实世界的模拟信号。第一步通常是从模拟转换到数字信号的形式通过抽样它使用一个模拟数字转换器（ADC），它变成了数字流的模拟信号。不过，通常情况下，所需的输出信号是另一个模拟输出信号，这需要一个数字至模拟转换器（DAC）。即使这个过程比模拟处理复杂，离散值范围内，计算能力为数字信号处理应用允许通过模拟处理诸多优点，在许多应用，如错误检测和校正，以及数据传输，压缩。

DSP算法一直运行在标准的计算机，专用处理器上所谓的数字信号处理器（DSP）或专用等特定应用集成电路（ASIC）的硬件。今天，有更多的数字信号处理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（主要用于工业，如马达控制应用程序）和流处理器使用等。

2.DSP的领域

在数字信号处理器中，数字信号的研究工程师通常在以下领域之一：时域（一维信号），空间域（多维信号），频域，自相关域和小波域。他们选择的域的处理由作出知情预测（或通过尝试不同的可能性），以最能代表该域的信号的本质特征的信号。一个从一个测量装置的样品顺序会产生一个时间或空间域表示，而一个离散傅立叶变换产生频域信息，那就是频谱。自相关被定义为交叉信号的相关性与本身在不同的时间或空间的间隔。

3.信号采样

主要文章：抽样（信号处理）

随着越来越多地使用计算机的使用情况和数字信号处理的需要有所增加。为了使用上，它必须与一个模拟数字转换器数字化计算机模拟信号。抽样通常分两个阶段进行，离散化和量化。在离散化阶段，对信号的空间划分为等价类和量化是由替换相应的等价类的代表信号的信号输出。在量化阶段，代表信号值是近似的值是从一个有限集合。

奈奎斯特- Shannon采样定理指出，一个信号可以准确地从它的采样中重建如果采样频率大于两倍的信号最高频率更高，但是需要无限多的样本。在实践中，采样频率往往大大超过两次，通过信号的有限带宽要求。

数字至模拟转换器是用来将数字信号转换回模拟信号。一个数字使用电脑是数字控制系统的关键要素。

4.时间和空间域

在时间或空间领域最常见的处理方法是，通过输入信号增强的方法称为过滤。数字滤波一般包括一些周边地区的一对输入或输出信号电流采样样本数线性变换。有多种方法过滤器的特点，例如：

?“线性”滤波器是输入采样的线性变换，其它过滤器是“非线性”。线性滤波器满足叠加的条件，即如果输入是线性加权组合不同的信号，输出同样是一个加权相应的输出信号的线性组合。

?“因果”过滤器使用的输入或输出信号唯一一次样品，而一个“非因果”滤波器使用未来的输入样本。阿非因果滤波器通常可以成为一个因果，增加了延迟地过滤改变。

?“时间不变”过滤器有固定属性随着时间的推移，诸如自适应滤波器及时更换其它过滤器。

?一些过滤器是“稳定”，别人是“不稳定的”。过滤器产生一个稳定的输出值收敛于一个常数随时间，或保持在一个有限区间范围内。一个不稳定的过滤器可以产生输出，没有界限的增长有界，甚至是零投入。

?“有限脉冲响应”（FIR）滤波器只使用输入信号，而一个“无限脉冲响应”滤波器（IIR）的同时使用输入信号和输出信号以前样本。FIR滤波器始终稳定，而IIR 滤波器可能不稳定。

过滤器可以由块，可以被用来推导出一个样加工算法实现过滤器的使用硬件指示图。过滤器也被描述为一个差分方程，零点和极点的集合，或者，如果它是一个FIR滤波器，脉冲响应或阶跃响应。

一个数字滤波器的任何给定的输入输出可能是计算卷积与输入信号的脉冲响应。

5.频域

信号转换从时间或空间域到频域通常通过傅里叶变换。傅里叶变换信号信息转换到每个频率分量的幅度和相位。通常，傅立叶变换转换为功率谱，这是每个频率分量幅度的平方。

对于在频域信号分析的目的，是最常见的信号特性分析。这位工程师可以研究的频谱，以确定哪些频率在输入信号存在以及哪些人失踪。

除了频率的信息，相位信息往往是需要的。这可从傅立叶变换。对于某些应用中，如何相频率变化可能是一个重要的考虑因素。

过滤，特别是在非实时的工作，也可以通过转换到频域，应用过滤器，然后转换回时域实现。这是一个快速，为O（n log n）运算，可以给任何过滤器形状基本上包括优秀近似砖墙滤波器。

还有一些常用的频域转换。例如，倒谱，通过转换为频域信号傅里叶变换，取对数，然后应用另一个傅里叶变换。这强调较小幅度的频率成分，而保留的频率元件数量级。

频域分析也称为频谱或频谱分析。

6.Z域分析

而模拟滤波器通常在s平面分析，数字滤波器，分析了在Z平面或Z域的Z -变换条件。

大多数过滤器可以说是在Z域（频域复数超）其传递函数。过滤器可分析在Z 域通过其零点和极点。

7.应用

DSP的主要应用是音频信号处理，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，地震学，生物医药。具体的例子是语音压缩和传输数字移动电话，房间匹配的高传真声音在电影和扩声应用，天气预报，经济预测，地震数据处理，分析和工业过程控制，计算机生成的动画均衡，医疗成像如CAT扫描和磁共振成像，MP3压缩，图像处理，高保真扬声器交叉和均衡，并可以使用音频效果与电吉他放大器。

8. 实施

数字信号处理往往是实现使用，如DSP56000的的TMS320，或SHARC处理器专门的微处理器。这些通常处理数据使用固定点算法，虽然有些版本可以方便使用浮点运算，而且更强大。为了更快地应用的FPGA [3]可能被使用。从2007年开始，多核DSP的实现已经开始，包括飞思卡尔和流处理器，等公司出现对于广大的使用速度更快的应用程序，可能会专门设计的专用集成电路。对于低速应用，传统的慢如微控制器处理器可能就足够了。也有越来越多DSP应用目前正在实施的嵌入式系统使用功能强大的PC与多核心处理器。