畢業(yè)設計(論文)外文資料翻譯系 ： 電子信息系 專 業(yè)： 電子信息科學與技術 姓 名： 學 號： 外文出處： DSP Design Line,Techonline Community, By Dr Iain A. Robin 附 件：1.外文資料翻譯譯文；2.外文原文 指導教師評語： 簽名： 年 月 日附件1：外文資料翻譯譯文數(shù)字濾波器簡介模擬和數(shù)字濾波器在信號處理過程中，濾波器的功能是去除信號中不需要的部分，如隨機噪聲，或者是提取信號中有用的部分，如包含在一定頻率范圍內的有用信號。下面的框圖表明了這一基本觀點：濾波器有兩種主要的類型：模擬濾波器和數(shù)字濾波器。他們的物質組成和工作原理都是完全不同的。模擬濾波器是由模擬電子電路組成的，如電阻、電感和運算放大器來產生所需的過濾效果。這樣的濾波器電路被廣泛應用在噪聲的降低、視頻信號的增強、音響系統(tǒng)中的圖像均衡以及其他的多個領域中。目前已經有很完善的技術標準來滿足一個已經提出要求的模擬濾波器電路的設計。在各個階段，過濾信號就是一個有物理量參與并且直接被模擬的電壓或電流量。一個數(shù)字濾波器使用數(shù)字處理器來執(zhí)行信號的采樣值的數(shù)值計算。該處理器可以是通用計算機，如PC機（個人電腦）或者是一個專用的數(shù)字信號處理芯片。模擬輸入信號必須先使用一個ADC（模擬到數(shù)字轉換器）采樣和數(shù)字化。由此產生代表連續(xù)采樣輸入信號值的二進制數(shù)字，是轉移到能夠對它們進行數(shù)值處理器上。這些計算通常都涉及乘以由常量與輸入信號相加的最終輸入值。如果需要，這些現(xiàn)在代表采樣的信號值濾波結果的計算，是由一個DAC（數(shù)字到模擬轉換器）輸出的信號轉換回模擬形式。請注意，在數(shù)字濾波中，信號是由一組數(shù)字序列，而不是電壓或電流。下圖顯示了一個這樣系統(tǒng)的基本設置：使用數(shù)字濾波器的優(yōu)點下面的列表給出了數(shù)字比模擬濾波器的一些主要優(yōu)點：1. 數(shù)字濾波器是可編程的，即它的操作決定與其存儲在處理器內存中的程序。這就意味著數(shù)字濾波器在不影響電路（硬件）的前提下可以很容易的被改變。模擬濾波器只能通過重新設計濾波器硬件電路來改變；2. 數(shù)字濾波器很容易設計，測試以及實行于通用計算機或工作站中；3. 模擬濾波電路的特點（特別是那些含有不穩(wěn)定性元件）受溫度漂移的影響并且依賴于溫度。而數(shù)字濾波器不受制于這些問題，因此對于溫度和時間，它極其的穩(wěn)定；4. 跟模擬濾波器不同，數(shù)字過濾器可以準確地處理低頻信號；隨著技術的DSP的速度繼續(xù)增加，數(shù)字過濾器被應用到高頻信號的RF（射頻）領域，這個在過去曾經是模擬技術專有的；5. 數(shù)字濾波器是非常靈活，他們具有以不同的方式來處理信號能力，這其中包括一些典型數(shù)字濾波器能夠適應信號按其特點變化而變化的能力；6. DSP處理器可以快速處理一系列由并聯(lián)或串聯(lián)級的等復雜組合的過濾器，與等效的模擬電路相比較，這使得硬件要求相對簡單、緊湊。數(shù)字濾波器的操作在本節(jié)中，我們將介紹數(shù)字濾波器運行的基本理論。這對于理解如何設計和使用數(shù)字濾波器是一個必不可少的。假設被數(shù)字化的“原始”信號以電壓波形的時間函數(shù)來描述：V = x(t)其中t代表時間。這個信號是以時間間隔h（采樣間隔）進行采樣的。其第i個信號的采樣值是時間t = i*h的函數(shù)：x i = x ( ih )因此由ADC至處理器轉換來的數(shù)字值就由下列的數(shù)字序列表示：x0 , x1 , x2 , x3 , . 信號的波形值與時間相對應：t = 0, h, 2h, 3h, .并且當t = 0時，開始采樣。在時間t = nh（其中n是正整數(shù)），將值x0 , x1 , x2 , x3 , . x n提供給處理器，并存儲在內存中。注意，采樣值xn+1, xn+2等是不可用的，因為他們還不存在。y0 , y1 , y2 , y3 , . y n 通常來說，數(shù)值y n是由x序列計算得到的。由y序列得到x序列的算法決定于具體的數(shù)字濾波器。在下一節(jié)，我們將看看一些簡單數(shù)字濾波器的例子。簡單數(shù)字濾波器 下面例子說明了數(shù)字濾波器的基本特征：1. 單位增益濾波器：每一個輸出值yn與輸入值xn 相等：y0= x0y1 =x1y2 =x2.etc這是一個經常用到的濾波器，濾波器對輸入信號沒有影響。2. 簡單的增益濾波器：y n = Kx n其中K是常數(shù)，該濾波器只使輸入信號有一個K倍的增益。當K > 1時，濾波器是一個放大器，當0 < K < 1時，它是一個衰減器，當K < 0時，對應的是一個反相器。上例1只是其的一種特殊的情況。3. 純延遲濾波器：y n = x n-1在t = nh時的輸出值只是簡單的等于t = (n-1)h時的輸入值，即信號延遲時間h：y0 = x-1y1 = x0y2 = x1y3 = x2. etc注意，由于抽樣是在t = 0 開始，輸入值x - 1 在t = -h是不確定的。因此一般假設在t = 0時（以及t = 0之前），輸出值都設為0。4. 差分濾波器：y n = x n - x n-1在t = nh時的輸出值等于當前輸入值xn與前一個輸入值xn-1的差值：即輸出值是最近一次采樣值間隔h輸入的變化。該濾波器對信號的影響就是類似于模擬電路中的微分電路。5. 均值濾波器：該輸出值是當前輸入值和前一個輸入值的平均值（算術平均）。這是一個簡單的低通濾波器，其通常將高頻中的信號過濾掉。（之后，我們將著眼于更有效的低通濾波器。）6. 三均值濾波器：該濾波器是當前的輸入值和先前兩個輸入值的均值，類似于先前的那個均值濾波器。類似于之前，x-1和x-2取0。7. 中心差分濾波器：該濾波器的濾波效果類似于例（4），輸出值等于當前輸入值與前兩個時間間隔h差值的二分之一。附件2：外文原文INTRODUCTION TO DIGITAL FILTERSAnalog and digital filtersIn signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.The following block diagram illustrates the basic idea.There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work.An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and opamps to produce the required filtering effect. Such filter circuits are widely used in such applications as noisereduction, video signal enhancement, graphic equalisers in hi-fi systems, and many other areas.There are well-established standard techniques for designing an analog filter circuit for a given requirement.At all stages, the signal being filtered is an electrical voltage or current which is the directanalogue of the physical quantity (e.g. a sound or video signal or transducer output) involved.A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialised DSP (Digital Signal Processor) chip.The analog input signal must first be sampled and digitised using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations,which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.The following diagram shows the basic setup of such a system.Advantages of using digital filtersThe following list gives some of the main advantages of digital over analog filters.1. A digital filter is programmable, i.e. its operation is determined by a program stored in the processorsmemory. This means the digital filter can easily be changed without affecting the circuitry (hardware).An analog filter can only be changed by redesigning the filter circuit.2. Digital filters are easily designed, tested and implemented on a general-purpose computer orworkstation.3. The characteristics of analog filter circuits (particularly those containing active components) aresubject to drift and are dependent on temperature. Digital filters do not suffer from these problems,and so are extremely stable with respect both to time and temperature.4. Unlike their analog counterparts, digital filters can handle low frequency signals accurately. As thespeed of DSP technology continues to increase, digital filters are being applied to high frequencysignals in the RF (radio frequency) domain, which in the past was the exclusive preserve of analogtechnology.5. Digital filters are very much more versatile in their ability to process signals in a variety of ways; thisincludes the ability of some types of digital filter to adapt to changes in the characteristics of thesignal.6. Fast DSP processors can handle complex combinations of filters in parallel or cascade (series),making the hardware requirements relatively simple and compact in comparison with the equivalentanalog circuitry.Operation of digital filtersIn this section, we will develop the basic theory of the operation of digital filters. This is essential to anunderstanding of how digital filters are designed and used.Suppose the "raw" signal which is to be digitally filtered is in the form of a voltage waveform described by the functionV = x(t)where t is time.This signal is sampled at time intervals h (the sampling interval). The sampled value at time t = ih isx i = x ( ih )Thus the digital values transferred from the ADC to the processor can be represented by the sequencex0 , x1 , x2 , x3 , . corresponding to the values of the signal waveform att = 0, h, 2h, 3h, .and t = 0 is the instant at which sampling begins.At time t = nh (where n is some positive integer), the values available to the processor, stored in memory, arex0 , x1 , x2 , x3 , . x nNote that the sampled values xn+1, xn+2 etc. are not available, as they havent happened yet!y0 , y1 , y2 , y3 , . y n In general, the value of yn is calculated from the values x0, x1, x2, x3, . , xn. The way in which the ys arecalculated from the xs determines the filtering action of the digital filter.In the next section, we will look at some examples of simple digital filters. Examples of simple digital filtersThe following examples illustrate the essential features of digital filters.1. Unity gain filter: Each output value yn is exactly the same as the corresponding input value xn:y0= x0y1 =x1y2 =x2.etcThis is a trivial case in which the filter has no effect on the signal.2. Simple gain filter:y n = Kx nwhere K = constant.This simply applies a gain factor K to each input value.K > 1 makes the filter an amplifier, while 0 < K < 1 makes it an attenuator. K < 0 corresponds to aninverting amplifier. Example (1) above is simply the special case where K = 1.3. Pure delay filter: y n = x n-1 The output value at time t = nh is simply the input at time t = (n-1)h, i.e. the signal is delayed by time h:y0 = x-1y1 = x0y2 = x1y3 = x2. etcNote that as sampling is assumed to commence at t = 0, the input value x-1 at t = -h is undefined. It isusual to take this (and any other values of x prior to t = 0) as zero.4.Two-term difference filter:y n = x n - x n-1The output value at t = nh is equal to the difference between the current input xn and the previousinput xn-1: i.e. the output is the change in the input over the most recent sampling interval h. The effect of thisfilter is similar to that of an analog differentiator circuit.5. Two-term average filter:The output is the average (arithmetic mean) of the current and previous input:This is a simple type of low pass filter as it tends to smooth out high-frequency variations in a signal.(We will look at more effective low pass filter designs later).6. Three-term average filter:This is similar to the previous example, with the average being taken of the current and two previousinputs: As before, x-1 and x-2 are taken to be zero. 7. Central difference filter:This is similar in its effect to example (4). The output is equal to half the change in the input signalover the previous two sampling intervals: