數(shù)字濾波器文獻(xiàn)翻譯.doc

文獻(xiàn)翻譯外文：Digital filterIn electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal (see digital signal processing). In an analog filter, the input signal is directly manipulated by the circuit.A digital filter system usually consists of an analog-to-digital converter to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Finally a digital-to-analog converter to complete the output stage. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized DSP with specific paralleled architecture for expediting operations such as filtering.Digital filters may be more expensive than an equivalent analog filter due to their increased complexity, but they make practical many designs that are impractical or impossible as analog filters. Since digital filters use a sampling process and discrete-time processing, they experience latency (the difference in time between the input and the response), which is almost irrelevant in analog filters.Digital filters are commonplace and an essential element of everyday electronics such as radios, cellphones, and stereo receivers.Characterization of digital filtersA digital filter is characterized by its transfer function, or equivalently, its difference equation. Mathematical analysis of the transfer function can describe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order low pass filter with a specific cut-off frequency), and then producing a transfer function which meets the specifications.The transfer function for a linear, time-invariant, digital filter can be expressed as a transfer function in the Z-domain; if it is causal, then it has the form: where the order of the filter is the greater of N or M. See Z-transforms LCCD equation for further discussion of this transfer function.This is the form for a recursive filter with both the inputs (Numerator) and outputs (Denominator), which typically leads to an IIR infinite impulse response behaviour, but if the denominator is made equal to unity i.e. no feedback, then this becomes an FIR or finite impulse response filter.Analysis techniquesA variety of mathematical techniques may be employed to analyze the behaviour of a given digital filter. Many of these analysis techniques may also be employed in designs, and often form the basis of a filter specification.Typically, one analyzes filters by calculating how the filter will respond to a simple input such as an impulse response. One can then extend this information to visualize the filters response to more complex signals. Riemann spheres have been used, together with digital video, for this purpose.Impulse responseThe impulse response, often denoted hk or hk, is a measurement of how a filter will respond to the Kronecker delta function. For example, given a difference equation, one would set x0 = 1 and xk = 0 for and evaluate. The impulse response is a characterization of the filters behaviour. Digital filters are typically considered in two categories: infinite impulse response (IIR) and finite impulse response (FIR). In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients: IIR filters on the other hand are recursive, with the output depending on both current and previous inputs as well as previous outputs. The general form of the an IIR filter is thus: Plotting the impulse response will reveal how a filter will respond to a sudden, momentary disturbance.Difference equationIn discrete-time systems, the digital filter is often implemented by converting the transfer function to a linear constant-coefficient difference equation (LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example: This is expanded: and divided by the highest order of z: The coefficients of the denominator, ak, are the feed-backward coefficients and the coefficients of the numerator are the feed-forward coefficients, bk. The resultant linear difference equation is: or, for the example above: rearranging terms: then by taking the inverse z-transform: and finally, by solving for yn: This equation shows how to compute the next output sample, yn, in terms of the past outputs, yn p, the present input, xn, and the past inputs, xn p. Applying the filter to an input in this form is equivalent to a Direct Form I or II realization, depending on the exact order of evaluation.Filter designMain article: Filter designThe design of digital filters is a deceptively complex topic.1 Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of much advanced research.There are two categories of digital filter: the recursive filter and the nonrecursive filter. These are often referred to as infinite impulse response (IIR) filters and finite impulse response (FIR) filters, respectively.2Filter realizationAfter a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.A given transfer function may be realized in many ways. Consider how a simple expression such as ax + bx + c could be evaluated one could also compute the equivalent x(a + b) + c. In the same way, all realizations may be seen as factorizations of the same transfer function, but different realizations will have different numerical properties. Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error. Some structures are better for fixed-point arithmetic and others may be better for floating-point arithmetic.Direct Form IA straightforward approach for IIR filter realization is Direct Form I, where the difference equation is evaluated directly. This form is practical for small filters, but may be inefficient and impractical (numerically unstable) for complex designs.3 In general, this form requires 2N delay elements (for both input and output signals) for a filter of order N.Direct Form IIThe alternate Direct Form II only needs N delay units, where N is the order of the filter potentially half as much as Direct Form I. This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays (z 1) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.The disadvantage is that Direct Form II increases the possibility of arithmetic overflow for filters of high Q or resonance.4 It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds.5 This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).Cascaded second-order sectionsA common strategy is to realize a higher-order (greater than 2) digital filter as a cascaded series of second-order biquadratric (or biquad) sections6 (see digital biquad filter). Advantages of this strategy is that the coefficient range is limited. Cascading direct form II sections result in N delay elements for filter order of N. Cascading direct form I sections result in N+2 delay elements since the delay elements of the input of any section (except the first section) are a redundant with the delay elements of the output of the preceding section.文獻(xiàn)翻譯譯文： 數(shù)字濾波 在電子學(xué)、計(jì)算機(jī)科學(xué)和數(shù)學(xué)中，數(shù)位濾波器是在一個(gè)系統(tǒng)上執(zhí)行一個(gè)采樣，在離散時(shí)間上對(duì)信號(hào)進(jìn)行的數(shù)學(xué)運(yùn)算，以減少或增加這種信號(hào)的某些方面。這不同于其他的電子過(guò)濾器，模擬濾波器是對(duì)一個(gè)連續(xù)時(shí)間模擬信號(hào)的進(jìn)行的工作。模擬信號(hào)可通過(guò)數(shù)字濾波處理，首先被數(shù)字化，并作為一個(gè)數(shù)字序列，然后操縱數(shù)學(xué)，然后重建為一個(gè)新的模擬信號(hào)（數(shù)字信號(hào)處理）的代表。在一個(gè)模濾波器，輸入信號(hào)為“直接”操縱電路。一個(gè)數(shù)字濾波器系統(tǒng)通常由模擬到數(shù)字轉(zhuǎn)換器輸入信號(hào)進(jìn)行采樣，通過(guò)一個(gè)微處理器和存儲(chǔ)器等存儲(chǔ)數(shù)據(jù)等一些周邊元件濾波系數(shù)之后最后由一個(gè)數(shù)字至模擬轉(zhuǎn)換器來(lái)完成輸出。程序指令（軟件）運(yùn)行在微處理器上執(zhí)行的數(shù)字通過(guò)執(zhí)行從ADC獲得必要的數(shù)學(xué)運(yùn)算的數(shù)字過(guò)濾器。在某些高性能應(yīng)用中，F(xiàn)PGA或ASIC是用來(lái)代替通用微處理器，或特定的加快，如過(guò)濾操作一個(gè)專門的DSP并行體系結(jié)構(gòu)。數(shù)字濾波器由于其復(fù)雜性增加可能比同等模擬濾波器昂貴，但他們實(shí)際是不切實(shí)際或不可能的許多設(shè)計(jì)中的模擬濾波器。由于數(shù)字過(guò)濾器使用一個(gè)采樣過(guò)程和離散時(shí)間處理，他們經(jīng)歷的延遲，這幾乎是在模擬過(guò)濾器無(wú)關(guān)（中之間的輸入和響應(yīng)時(shí)間的差異）。數(shù)字濾波器是司空見慣的日常電子產(chǎn)品及如收音機(jī)，手機(jī)和立體聲接收器的基本要素。表征數(shù)字濾波器一個(gè)數(shù)字濾波器的特點(diǎn)是它的傳遞函數(shù)，或等價(jià)地，它的差分方程。數(shù)學(xué)的傳遞函數(shù)分析，可以描述它會(huì)回應(yīng)任何輸入。因此，設(shè)計(jì)一個(gè)合適的過(guò)濾器規(guī)格發(fā)展的問(wèn)題包括（例如，一個(gè)二階低通濾波器，具體截止頻率），然后產(chǎn)生一個(gè)傳輸功能，符合規(guī)范。一類線性時(shí)不變的傳遞函數(shù)，數(shù)字濾波器可以表示為一個(gè)在Z域傳遞函數(shù)，如果它有因果關(guān)系，那么它有以下形式：在過(guò)濾器的順序是N或M見Z變換的LCCD方程為這個(gè)傳遞函數(shù)的進(jìn)一步討論更大。這是一個(gè)遞歸的形式同時(shí)與輸入（分母）和輸出（分母），這通常會(huì)導(dǎo)致無(wú)限脈沖響應(yīng)的IIR行為，但如果分母是由平等團(tuán)結(jié)即沒(méi)有反饋濾波器，那么這將成為一個(gè)區(qū)或有限脈沖響應(yīng)濾波器。分析技術(shù)一個(gè)數(shù)理可以采用多種方法來(lái)分析一個(gè)給定的行為數(shù)字濾波器。這些分析技術(shù)很多人可能還受聘于設(shè)計(jì)，往往形成了一個(gè)過(guò)濾器規(guī)范的基礎(chǔ)。通常情況下，計(jì)算分析了一個(gè)過(guò)濾器將如何應(yīng)對(duì)，如脈沖響應(yīng)一個(gè)簡(jiǎn)單的輸入過(guò)濾器。一個(gè)可以拓展這些信息可視化的過(guò)濾器的反應(yīng)更復(fù)雜的信號(hào)。黎曼球已被使用，加上數(shù)字視頻，用于這一目的。脈沖響應(yīng)脈沖響應(yīng)，通常記 k的或港幣，是如何過(guò)濾器將響應(yīng)克羅內(nèi)克函數(shù)的測(cè)量。例如，給出一個(gè)差分方程，一會(huì)成立為x0 = 1與xk = 0 和評(píng)估的。脈沖響應(yīng)是一個(gè)過(guò)濾器的行為表征。數(shù)字濾波器通常被認(rèn)為兩類：無(wú)限脈沖響應(yīng)（IIR）和有限脈沖響應(yīng)（FIR）。在線性時(shí)不變FIR濾波器的情況下，脈沖響應(yīng)恰好等于濾波器系數(shù)的順序：另一方面IIR濾波器的遞歸，輸出與當(dāng)前和以前的輸入以及先前輸出而定。該IIR濾波器的一般形式是這樣的： 繪制了脈沖響應(yīng)濾波器將揭示如何將響應(yīng)突然，瞬間干擾。差分方程在離散時(shí)間系統(tǒng)，數(shù)字濾波通常是通過(guò)實(shí)施轉(zhuǎn)化的Z變換，傳遞函數(shù)為線性常系數(shù)差分方程（LCCD）。離散頻域傳遞函數(shù)可以寫成兩個(gè)多項(xiàng)式之比。例如：這是擴(kuò)大：和除以最高的Z順序：與分母，支AK的系數(shù)，是飼料落后的系數(shù)和分子的系數(shù)是饋系數(shù)，淺灘。由此