【正文】 在暗示，映射函數(shù)應(yīng)該是這樣的： 虛（ j）在 s 平面軸映射到的 Z平面圓。 一個穩(wěn)定的信號傳遞函數(shù)轉(zhuǎn)化為一個穩(wěn)定的數(shù)字 傳輸功能。 為此，使用最廣泛的變革是雙線性變換在 。 不像 IIR 數(shù)字濾波器設(shè)計， FIR 濾波器的設(shè)計沒有任何的模擬濾波器的設(shè)計連接。 。 作者： Sanjit 國籍： USA 出處： Digital Signal Processing A ComputerBased Approach 3e FIR Digital Filter Design 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. 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 z1 and is thus always guaranteed stable. In this chapter, we consider the FIR digital filter design problem. Unlike the IIR digital filter design problem, it is always possible to design FIR digital filters with exact linearphase. First ,we describe a popular approach to the design of FIR digital filters with linearphase. We then consider the puteraided design of linearphase FIR digital filters. To this end, we restrict our discussion to the use of matlab in determining the transfer functions. Since the order of the FIR transfer function is usually much higher than that of an IIR transfer function meeting the same frequency response specifications, we outline two methods for the design of putationally efficient FIR digital filters requiring fewer multipliers than a direct form realization. Finally, we present a method of designing a minimumphase FIR digital filter that leads to a transfer function with smaller group delay than that of a linearphase equivalent. The minimumphase FIR digital filter is thus attractive in applications where the linearphase requirement is not an issue. preliminary considerations In this section,we first review some basic approaches to the design of FIR digital filters and the determination of the filter order to meet the prescribed specifications. Basic Approaches to FIR Digital Filter Design 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 specified 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 z1 of degree N: ???? NnnznhzH0 ][)( () The corresponding frequency response is given by ???? Nnnjj enheH0 ][)(?? () It has been shown in section that any finite duration sequence x[n] of length N+1 is pletely characterized by N+1 samples of its discretetime Fourier transform X? ??je . As a result, the design of an FIR filter of length N+1 can be acplished by finding either the impulse response sequence {h[n]} or N+1 samples of its frequency response H ? ??je . Also ,to ensure a linearphase design, the condition ][][ nNhnh ??? , must be satisfied. Two direct approaches to the design of FIR filters are the windowed Fourier series approach and the frequency sampling approach. We describe the former approach in Section . The second approach is treated in Problems and . In section , we outline puterbased digital filter design methods. Estimation of the Filter Order After the type of the digital filter has selected, the next step in the filter design process is to estimate the filter order should be the smallest integer greater than or equal to the estimated value. FIR Digital Filter Order Estimation For 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 angular frequency p? , normalizef stopband edge angular frequency s? , peak passband ripple p? ,and peak stopband ripple s? . We review three such formulas. Kaiser39。s Formula. A rather simple formula developed by Kaiser [Kai74] is given by ?????2/)(13)(log20 10psspN ? ??? . We illustrate the application of the above formula in Example . Bellanger39。s Formula. Another simple formula advanced by Bellanger is given by [Bel81] Preliminary Considerations 12/)(3 )10(log2 10 ???? ??? ??ps spN. Its application is considered in Example . Hermann39。s Formula. The formula due to Hermann et al.[Her73] gives a slightly more accurate value for the order and is given by ??? ??????? 2/)( ]2/))[(,(,2ppspssps FDN ? ??? ? ）（ , Where ]6)(l o g5)(l o g4[l o g]3)(l o g2)(l o g1[),( 102101010210 aaaaaaD ppsppsp ??????? ??????? , And ]lo g[ lo g21),( 1010 spsp bbF ???? ??? , With a1=, a2= ,a3=, a4=, a5=, a6=, b1=, b2=. The formula given in Eq.() is valid for s???p . If sp ?? ? , then the filter order formula to be used i