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1、數(shù)字信號處理一、導(dǎo)論數(shù)字信號處理(DSP)是由一系列的數(shù)字或符號來表示這些信號的處理的過程的。數(shù)字信號處理與模擬信號處理屬于信號處理領(lǐng)域。DSP包括子域的音頻和語音信號處理,雷達(dá)和聲納信號處理,傳感器陣列處理,譜估計(jì),統(tǒng)計(jì)信號處理,數(shù)字圖像處理,通信信號處理,生物醫(yī)學(xué)信號處理,地震數(shù)據(jù)處理等。由于DSP的目標(biāo)通常是對連續(xù)的真實(shí)世界的模擬信號進(jìn)行測量或?yàn)V波,第一步通常是通過使用一個模擬到數(shù)字的轉(zhuǎn)換器將信號從模擬信號轉(zhuǎn)化到數(shù)字信號。通常,所需的輸出信號卻是一個模擬輸出信號,因此這就需要一個數(shù)字到模擬的轉(zhuǎn)換器。即使這個過程比模擬處理更復(fù)雜的和而且具有離散值,由于數(shù)字信號處理的錯誤檢測和校正不易受噪聲
2、影響,它的穩(wěn)定性使得它優(yōu)于許多模擬信號處理的應(yīng)用(雖然不是全部)。DSP算法一直是運(yùn)行在標(biāo)準(zhǔn)的計(jì)算機(jī),被稱為數(shù)字信號處理器(DSP)的專用處理器或在專用硬件如特殊應(yīng)用集成電路(ASIC)。目前有用于數(shù)字信號處理的附加技術(shù)包括更強(qiáng)大的通用微處理器,現(xiàn)場可編程門陣列(FPGA),數(shù)字信號控制器(大多為工業(yè)應(yīng)用,如電機(jī)控制)和流處理器和其他相關(guān)技術(shù)。在數(shù)字信號處理過程中,工程師通常研究數(shù)字信號的以下領(lǐng)域:時間域(一維信號),空間域(多維信號),頻率域,域和小波域的自相關(guān)。他們選擇在哪個領(lǐng)域過程中的一個信號,做一個明智的猜測(或通過嘗試不同的可能性)作為該域的最佳代表的信號的本質(zhì)特征。從測量裝置對樣品
3、序列產(chǎn)生一個時間或空間域表示,而離散傅立葉變換產(chǎn)生的頻譜的頻率域信息。自相關(guān)的定義是互相關(guān)的信號本身在不同時間間隔的時間或空間的相關(guān)情況。二、信號采樣隨著計(jì)算機(jī)的應(yīng)用越來越多地使用,數(shù)字信號處理的需要也增加了。為了在計(jì)算機(jī)上使用一個模擬信號的計(jì)算機(jī),它上面必須使用模擬到數(shù)字的轉(zhuǎn)換器(ADC)使其數(shù)字化。采樣通常分兩階段進(jìn)行,離散化和量化。在離散化階段,信號的空間被劃分成等價類和量化是通過一組有限的具有代表性的信號值來代替信號近似值。奈奎斯特-香農(nóng)采樣定理指出,如果樣本的取樣頻率大于兩倍的信號的最高頻率,一個信號可以準(zhǔn)確地重建它的樣本。在實(shí)踐中,采樣頻率往往大大超過所需的帶寬的兩倍。數(shù)字模擬轉(zhuǎn)換
4、器(DAC)用于將數(shù)字信號轉(zhuǎn)化到模擬信號。數(shù)字計(jì)算機(jī)的使用是數(shù)字控制系統(tǒng)中的一個關(guān)鍵因素。三、時間域和空間域在時間或空間域中最常見的處理方法是對輸入信號進(jìn)行一種稱為濾波的操作。濾波通常包括對一些周邊樣本的輸入或輸出信號電流采樣進(jìn)行一些改造?,F(xiàn)在有各種不同的方法來表征的濾波器,例如:一個線性濾波器的輸入樣本的線性變換;其他的過濾器都是“非線性”。線性濾波器滿足疊加條件,即如果一個輸入不同的信號的加權(quán)線性組合,輸出的是一個同樣加權(quán)線性組合所對應(yīng)的輸出信號?!耙蚬睘V波器只使用以前的樣本的輸入或輸出信號;而“非因果”濾波器使用未來的輸入樣本。一個非因果濾波器通??梢酝ㄟ^增加一個延遲將它變成了一個因果
5、濾波器?!皶r間不變”濾波器隨著時間的推移性具有穩(wěn)定特性;其他濾波器如隨時間變化的自適應(yīng)濾波器。一些濾波器是“穩(wěn)定”的,別的是“不穩(wěn)定的”。一個穩(wěn)定的濾波器產(chǎn)生的輸出信號隨時間收斂于一個恒定值,或在一個有限的時間間隔內(nèi)是有界的。一種不穩(wěn)定的濾波器可以產(chǎn)生一個沒有增長界限的輸出,甚至零輸入有界?!坝邢廾}沖響應(yīng)(FIR)” 濾波器只使用于輸入信號,而“無限脈沖響應(yīng)濾波器(IIR)”使用于輸入信號和輸出信號之前的樣品。FIR濾波器總是穩(wěn)定的,而IIR濾波器可能是不穩(wěn)定的。大多數(shù)濾波器可以被描述在z域(頻域的一個超集)的傳遞函數(shù)。如果它是一個FIR濾波器的脈沖響應(yīng)和階躍響應(yīng),濾波器也可以被描述為一個差分
6、方程,或?qū)α泓c(diǎn)和極點(diǎn)的收集。一個FIR濾波器的輸出是通過對任何給定的輸入與脈沖響應(yīng)的卷積計(jì)算得到的。濾波器也可以被用來推導(dǎo)出一個樣品的處理算法的方塊圖利用硬件指令實(shí)現(xiàn)濾波器所代表。四、頻域信號通常是通過傅立葉變換將其從時間或空間域轉(zhuǎn)換到頻率域。傅里葉變換將信號轉(zhuǎn)換信息和相位分量級的每個頻率。通常的傅里葉變換轉(zhuǎn)換為功率譜,這是大小的每個頻率分量的平方。在頻域?qū)π盘柗治龅淖畛R姷挠猛臼切盘柼匦苑治?。工程師可以研究頻譜來確定哪一頻率的存在于輸入信號中。濾波,特別是在非實(shí)時的工作也可以被轉(zhuǎn)換到頻域?qū)崿F(xiàn),應(yīng)用濾波器,然后轉(zhuǎn)換回時域。這是一個快速,O(nlogn)操作,可以基本上給出任何濾波器的形狀包括磚
7、墻濾波器優(yōu)良的逼近。有一些常用的頻域變換。例如,倒譜轉(zhuǎn)換信號的頻域傅立葉變換,取對數(shù),然后將另一個傅里葉變換。這強(qiáng)調(diào)的頻率成分的幅度較小而保留的頻率分量的大小順序。頻域分析又稱譜或譜分析。五、信號處理信號通常需要以不同的方式進(jìn)行處理。例如,從一個傳感器的輸出信號可能被污染的多余電“噪音”。電極連接到一個病人的胸部時,心電圖是測量由心臟和其他肌肉的活動引起的微小的電壓變化。由于電的干擾從電源的強(qiáng)烈影響,信號通常是采用“總管拾取”。處理信號的濾波電路可以消除或至少降低信號的不需要的部分?,F(xiàn)在,越來越多的的情況下,是由DSP技術(shù)來進(jìn)行信號的濾波以提高信號質(zhì)量或提取重要信息,而不是模擬電子技術(shù)。六、D
8、SP的發(fā)展數(shù)字信號處理的發(fā)展從1960年代的大型數(shù)字計(jì)算機(jī)的數(shù)字運(yùn)算應(yīng)用程序的使用快速傅立葉變換(FFT),它允許一個信號的頻譜可以快速計(jì)算。這些技術(shù)在當(dāng)時沒有被廣泛使用,因?yàn)楹线m的計(jì)算設(shè)備通常僅在大學(xué)及其他科研機(jī)構(gòu)可以使用。七、數(shù)字信號處理器(DSP)在20世紀(jì)70年代末和20世紀(jì)80年代初微處理機(jī)的介紹使DSP技術(shù)在更廣泛的范圍內(nèi)得到了使用。然而,通用微處理器如Intel x86的家庭并不適合于DSP的計(jì)算密集型的需求,隨著20世紀(jì)80年代DSP重要性的增加導(dǎo)致幾個主要的電子產(chǎn)品制造商(如德克薩斯儀器,模擬設(shè)備和摩托羅拉)去開發(fā)數(shù)字信號處理器芯片,專門的微處理器,專門設(shè)計(jì)用于在數(shù)字信號處理
9、要求的操作的類型的架構(gòu)。(注意,縮寫DSP數(shù)字信號處理的不同的意思,這個詞用于處理數(shù)字信號,多種技術(shù)或數(shù)字信號處理器,一種特殊類型的微處理器芯片)。像一個通用微處理器,DSP是一種具有其自己的本地指令代碼的可編程器件。DSP芯片是能夠每秒進(jìn)行數(shù)以百萬計(jì)的浮點(diǎn)運(yùn)算,像他們同類型的更著名的通用器件,更快和更強(qiáng)大的版本正在不斷被引入。DSP也可以嵌入在復(fù)雜的“系統(tǒng)芯片”裝置,通常包括模擬和數(shù)字電路。8、數(shù)字信號處理器的應(yīng)用DSP技術(shù)是當(dāng)今普遍在手機(jī),多媒體計(jì)算機(jī),錄像機(jī),CD播放器,硬盤驅(qū)動器和控制器的調(diào)制解調(diào)器等設(shè)備,并將很快在電視和電話業(yè)務(wù)中取代模擬電路。DSP的一個重要的應(yīng)用是信號的壓縮和解壓
10、。信號壓縮用于數(shù)字蜂窩電話,在每一個地方的“單元”讓更多的電話同時被處理。DSP信號壓縮技術(shù)不僅使人們可以相互交談,而且可以通過使用安裝在計(jì)算機(jī)上的小的攝像機(jī)使人們通過顯示器看見對方,而這些只需要將傳統(tǒng)的電話線連接在一起。在音頻CD系統(tǒng),DSP技術(shù)來執(zhí)行復(fù)雜的錯誤檢測和校正原始數(shù)據(jù),因?yàn)樗菑墓獗P讀取。雖然一些潛在的DSP技術(shù)的數(shù)學(xué)理論,如傅立葉和希爾伯特變換,數(shù)字濾波器的設(shè)計(jì)和信號壓縮,可以相當(dāng)復(fù)雜,而數(shù)值運(yùn)算所需的實(shí)際實(shí)現(xiàn)這些技術(shù)是非常簡單的,主要包括操作可以在一個便宜的四功能的計(jì)算器上進(jìn)行操作。一種DSP芯片的結(jié)構(gòu)設(shè)計(jì)進(jìn)行這樣的操作非???,處理的樣品每秒數(shù)以億計(jì),提供實(shí)時的性能:即,能夠
11、處理一個實(shí)時的信號,因?yàn)樗遣蓸?,然后輸出信號的處理,例如揚(yáng)聲器或視頻顯示。所有的DSP應(yīng)用前面提到的實(shí)例,如硬盤驅(qū)動器和移動電話,要求實(shí)時操作。主要電子產(chǎn)品制造商已投入巨資在DSP技術(shù)。因?yàn)樗麄儸F(xiàn)在發(fā)現(xiàn)在大眾市場的產(chǎn)品應(yīng)用中,DSP芯片的電子裝置占有世界市場的很大比例。銷售額每年數(shù)十億美元,并可能繼續(xù)快速增長。DSP主要應(yīng)用的音頻信號處理,音頻壓縮,數(shù)字圖像處理,視頻壓縮,語音處理,語音識別,數(shù)字通信,雷達(dá),聲納,地震,和生物醫(yī)學(xué)。具體的例子是在數(shù)字移動電話的語音壓縮與傳輸,空間匹配均衡的音響、擴(kuò)聲領(lǐng)域,良好的天氣預(yù)測,經(jīng)濟(jì)預(yù)測,地震數(shù)據(jù)處理,和工業(yè)過程控制分析,計(jì)算機(jī)生成的動畫電影中,醫(yī)學(xué)
12、影像如CAT掃描和MRI,MP3壓縮,圖像處理,高保真度揚(yáng)聲器分頻器和均衡,并與電吉他放大器使用的音頻效果。九、數(shù)字信號處理的實(shí)驗(yàn)數(shù)字信號處理是經(jīng)常使用專門的微處理器,如dsp56000,TMS320,或SHARC。這些通常處理數(shù)據(jù)使用定點(diǎn)運(yùn)算,雖然某些版本可以使用浮點(diǎn)算法和更強(qiáng)大。更快的應(yīng)用FPGA可能從慢啟動流處理器應(yīng)用Freescale公司的出現(xiàn),傳統(tǒng)的較慢的處理器如單片機(jī)可能是適當(dāng)?shù)??!居⑽脑摹緿igital Signal Processing1、IntroductionDigital signal processing (DSP) is concerned with the rep
13、resentation 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 arr
14、ay 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
15、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 val
16、ue 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 processo
17、rs 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)
18、, 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 do
19、main, 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 prod
20、uces 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 SamplingWith the
21、 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 discre
22、tization 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 fro
23、m 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
24、 signal. The use of a digital computer is a key ingredient in digital control systems.3 、Time and Space DomainsThe most common processing approach in the time or space domain isenhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a
25、 number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters, for example: A “l(fā)inear” filter is a linear transformation of input samples; other filters are “non-linear.” Linear filters satisfy the superposition condition, i.e.
26、 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-causa
27、l 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 con
28、stant 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 us
29、es 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 t
30、ransfer 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. Fi
31、lters 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 DomainSignals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Four
32、ier 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 an
33、alysis of signal properties. The engineer can study the spectrum to determine which frequencies are presentin 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
34、to the time domain. This is a fast, O (nlogn) 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 transf
35、orm, takes thelogarithm, 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 ProcessingSignals commonly
36、 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 patients chest when an ECG is taken measure tiny electrical voltage changes due to the activity of the heart and other
37、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
38、 or to extract important information is done by DSP techniques rather than by analog electronics.6、Development of DSPThe development of digital signal processing dates from the 1960s with the use of mainframe digital computers number-crunching applications such an the Fast Fourier Transform (FFT), w
39、hich 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
40、 the microprocessor in the late 1970s and early 1980s 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 19
41、80s 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 sig
42、nal 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 programmab
43、le 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 “s
44、ystem-on-chip” devices, often containing both analog and digital circuitry.8、Applications of DSPDSP 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 i
45、n 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 behandled simultaneously within each local “cell”. DSP signal compression technology allows people not onl
46、y 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 t
47、he 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 sim
48、ple, 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 “l(fā)ive” 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 dr
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