外文翻譯---fir數(shù)字濾波器的設(shè)計(jì)

1、<p>　　FIR Digital Filter Design </p><p>　　In chapter 9 we considered the design of IIR digital filters. For such filters, it is also necessary to ensure that the derived transfer function G(z) is stable

2、. On the other hand, in the case of FIR digital filter design,the stability is not a design issue as the transfer function is a polynomial in z-1 and is thus always guaranteed stable. In this chapter, we consider the FIR

3、 digital filter design problem.</p><p>　　Unlike the IIR digital filter design problem, it is always possible to design FIR digital filters with exact linear-phase. First ,we describe a popular approach to th

4、e design of FIR digital filters with linear-phase. We then consider the computer-aided design of linear-phase FIR digital filters. To this end, we restrict our discussion to the use of matlab in determining the transfer

5、functions. Since the order of the FIR transfer function is usually much higher than that of an IIR transfer functi</p><p>　　10.1 preliminary considerations </p><p>　　In this section,we first rev

6、iew some basic approaches to the design of FIR digital filters and the determination of the filter order to meet the prescribed specifications. </p><p>　　10.1.1 Basic Approaches to FIR Digital Filter Design&

7、lt;/p><p>　　Unlike IIR digital filter design, FIR filter design does not have any connection with the design of analog filters. The design of FIR filters is therefore based on a direct approximation of the spec

8、ified magnitude response,with the often added requirement that the phase response be linear. Recall a causal FIR transfer function H(z) of length N+1 is a polynomial in z-1 of degree N:</p><p><b>　　(10

9、.1)</b></p><p>　　The corresponding frequency response is given by</p><p><b>　　(10.2)</b></p><p>　　It has been shown in section 5.3.1 that any finite duration seque

10、nce x[n] of length N+1 is completely characterized by N+1 samples of its discrete-time Fourier transform X. As a result, the design of an FIR filter of length N+1 can be accomplished by finding either the impulse respons

11、e sequence {h[n]} or N+1 samples of its frequency response H. Also ,to ensure a linear-phase design, the condition </p><p><b>　　,</b></p><p>　　must be satisfied. Two direct approache

12、s to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section 10.2. The second approach is treated in Problems 10.31 and 10.32. In

13、 section 10.3, we outline computer-based digital filter design methods.</p><p>　　10.1.2 Estimation of the Filter Order </p><p>　　After the type of the digital filter has selected, the next step

14、in the filter design process is to estimate the filter order should be the smallest integer greater than or equal to the estimated value.</p><p>　　FIR Digital Filter Order Estimation </p><p>　　F

15、or the design of lowpass FIR digital filters, several authors have advanced formulas for estimating the minimum value of the filter order N directly from the digital filter specifications: normalized passband edge angula

16、r frequency , normalizef stopband edge angular frequency , peak passband ripple ,and peak stopband ripple . We review three such formulas.</p><p>　　Kaiser's Formula. A rather simple formula developed by

17、Kaiser [Kai74] is given by</p><p><b>　　.</b></p><p>　　We illustrate the application of the above formula in Example 10.1.</p><p>　　Bellanger's Formula. Another simpl

18、e formula advanced by Bellanger is given by [Bel81]</p><p>　　10.1 Preliminary Considerations</p><p><b>　　.</b></p><p>　　Its application is considered in Example 10.2.<

19、;/p><p>　　Hermann's Formula. The formula due to Hermann et al.[Her73] gives a slightly more accurate value for the order and is given by </p><p><b>　　,</b></p><p><b

20、>　　Where</b></p><p><b>　　,</b></p><p><b>　　And</b></p><p><b>　　,</b></p><p><b>　　With </b></p><p>

21、　　a1=0.005309, a2=0.07114 ,a3=-0.4761,</p><p>　　a4=0.00266, a5=0.5941, a6=0.4278,</p><p>　　b1=11.01217, b2=0.51244.</p><p>　　The formula given in Eq.(10.5) is valid for . I

22、f , then the filter order formula to be used is obtained by interchanging and in Eq.(10.6a) and (10.6b).</p><p>　　For small values of and , all of the above formulas provide reasonably close and accurate

23、results. On the other hand, when the values of and are large, Eq.(10.5) yields a more accurate value for the order.</p><p>　　A Comparison of FIR Filter Order Formulas</p><p>　　Note that the fi

24、lter order computed in Examples 10.1, 10.2 and 10.3, using Eqs.(10.3),(10.3),and (10.5),</p><p>　　Respectively ,are all different. Each of these three formulas provide only an estimate of the required filter

25、 order. The frequency response of the FIR filter designed using this estimated order may or may not meet the given specifications. If the specifications are not met, it is recommended that the filter order be gradually i

26、ncreased until the specifications are met. Estimation of the FIR filter order using MATLAB is discussed in Section 10.5.1.</p><p>　　An important property of each of the above three formulas is that the estim

27、ated filter order N of the FIR filter is inversely proportional to the transition band width () and does not depend on the actual location of the transition band. This implies that a sharp cutoff FIR filter with a narrow

28、 transition band would be of very high order, whereas an FIR filter with a wide transition band will have a very low order. </p><p>　　Another interesting property of Kaiser's and Bellanger's formulas

29、 is that the order depends on the product . This implies that if the values of and are interchanged, the order remains the same.</p><p>　　To compare the accuracy of the the above formulas, we estimate usin

30、g each formula the order of three linear-phase lowpass FIR filters of known order, bandedges, and ripples. The specifications of the three filters are as follows:</p><p>　　Filter No.1: </p><p>

31、　　Filter No.2: </p><p>　　Filter No.3: .</p><p>　　The results are given in Table 10.1.</p><p>　　Each one of the three formulas given above can also be used to estimate the order o

32、f highpass, bandpass, and bandstop FIR filters. In the case of the bandpass and bandstop filters, there are two transition bands. It has been found that here the filter order basically depends on the transition band with

33、 the smallest width. We illustrate the use of the Kasier's formula in estimating the order of a linear-phase bandpass FIR filter in Example 10.4.</p><p>　　作者：Sanjit K.Mitra</p><p><b>　

34、　國(guó)籍：USA</b></p><p>　　出處：Digital Signal Processing -A Computer-Based Approach 3e</p><p>　　FIR數(shù)字濾波器的設(shè)計(jì) </p><p>　　在第9章，我們考慮了IIR數(shù)字濾波器的設(shè)計(jì)。對(duì)于這樣的過濾器，它也必須確保派生傳遞函數(shù)G（z）是穩(wěn)定的。另一方面，在FI

35、R數(shù)字濾波器設(shè)計(jì)的情況下，穩(wěn)定是不是設(shè)計(jì)問題，因?yàn)閭鬟f函數(shù)是一個(gè)在z-1的多項(xiàng)式，因而始終保證穩(wěn)定。在這一章中，我們考慮的FIR數(shù)字濾波器的設(shè)計(jì)問題。 不同的是IIR數(shù)字濾波器設(shè)計(jì)問題，它總是可以設(shè)計(jì)一種精確的FIR線性相位數(shù)字濾波器。首先，我們描述了發(fā)展與線性相位FIR數(shù)字濾波器設(shè)計(jì)流行的方法。然后，我們考慮線性相位FIR數(shù)字濾波器的計(jì)算機(jī)輔助設(shè)計(jì)。為此，我們限制我們討論了MATLAB在確定傳遞函數(shù)的使用。自區(qū)傳遞函數(shù)順序通常

36、比轉(zhuǎn)移的IIR會(huì)議相同的頻率響應(yīng)規(guī)格功能還高，我們概述了計(jì)算效率比直接的FIR需要較少的乘法器實(shí)現(xiàn)形式的數(shù)字濾波器設(shè)計(jì)的兩種方法。最后，我們提出一個(gè)設(shè)計(jì)最低FIR數(shù)字濾波器的相位，導(dǎo)致一個(gè)比一個(gè)更小的線性相位延遲相當(dāng)于該組的傳遞函數(shù)方法。最小相位FIR數(shù)字濾波器因此，在應(yīng)用中的線性相位的要求是沒有問題的吸引力。10.1初步考慮在本節(jié)中，我們第一次審查的FIR數(shù)字濾波器的設(shè)計(jì)和定階濾波器，以滿足規(guī)范規(guī)定的一些基本方法。10.1.1基