【正文】 對(duì)比f(wàn)igure（1）和figure（4）濾波前后的波形和頻譜，可以看到波形得到了重現(xiàn)②濾波器的采樣頻率為22050Hz，濾波器的階數(shù)為24③，④阻帶衰減為40dB，參考文獻(xiàn)[1]，2006[2]徐明遠(yuǎn)，[3]鄒鯤，袁俊泉， [4]張明照，劉政波，[5]劉波，[6]William , Shanmugan,Theodore ,Kurt ，楊光松，許芳，[7][8]Oppenheim A V,Schafer R Signal Processing. Prentice Hall,[9][10]蘇金明，張蓮花，附錄附錄一 外文原文及翻譯外文原文FIR Filter Design TechniquesAbstractThis report deals with some of the techniques used to design FIR filters. In the beginning, the windowing method and the frequency sampling methods are discussed in detail with their merits and demerits. Different optimization techniques involved in FIR filter design are also covered, including Rabiner’s method for FIR filter design. These optimization techniques reduce the error caused by frequency sampling technique at the nonsampled frequency points. A brief discussion of some techniques used by filter design packages like Matlab are also included. Introduction FIR filters are filters having a transfer function of a polynomial in z and is an allzero filter in the sense that the zeroes in the zplane determine the frequency response magnitude z transform of a Npoint FIR filter is given by (1)FIR filters are particularly useful for applications where exact linear phase response is required. The FIR filter is generally implemented in a nonrecursive way which guarantees a stable filter. FIR filter design essentially consists of two parts (i) approximation problem (ii) realization problem The approximation stage takes the specification and gives a transfer function through four steps. They are as follows:(i) A desired or ideal response is chosen, usually in the frequency domain. (ii) An allowed class of filters is chosen ( length N for a FIR filters). (iii) A measure of the quality of approximation is chosen. (iv) A method or algorithm is selected to find the best filter transfer function. The realization part deals with choosing the structure to implement the transfer function which may be in the form of circuit diagram or in the form of a program.There are essentially three wellknown methods for FIR filter design namely: (1) The window method (2) The frequency sampling technique (3) Optimal filter design methods The Window Method In this method, [Park87], [Rab75], [Proakis00] from the desired frequency response specification Hd(w), corresponding unit sample response hd(n) is determined using the following relation (2) (3)In general, unit sample response hd(n) obtained from the above relation is infinite in duration, so it must be truncated at some point say n= M1 to yield an FIR filter of length M (. 0 to M1). This truncation of hd(n) to length M1 is same as multiplying hd(n) by the rectangular window defined as w(n) = 1 0≦n≦M1 (4)0 otherwiseThus the unit sample response of the FIR filter bees h(n) = hd(n) w(n) (5) = hd(n) 0≦n≦M1= 0 otherwise Now, the multiplication of the window function w(n) with hd(n) is equivalent to convolution of Hd(w) with W(w), where W(w) is the frequency domain representation of the window function (6)Thus the convolution of Hd(w) with W(w) yields the frequency response of the truncated FIR filter (7)The frequency response can also be obtained using the following relation (8)But direct truncation of hd(n) to M terms to obtain h(n) leads to the Gibbs phenomenon effect which manifests itself as a fixed percentage overshoot and ripple before and after an approximated discontinuity in the frequency response due to the nonuniform convergence of the fourier series at a the frequency response obtained by using (8) contains ripples in the frequency domain. In order to reduce the ripples, instead of multiplying hd(n) with a rectangular window w(n), hd(n) is multiplied with a window function that contains a taper and decays toward zero gradually, instead of abruptly as it occurs in a rectangular window. As multiplication of sequences hd(n) and w(n) in time domain is equivalent to convolution of Hd(w) and W(w) in the frequency domain, it has the effect of smoothing Hd(w). The several effects of windowing the Fourier coefficients of the filter on the result of the frequency response of the filter are as follows: (i) A major effect is that discontinuities in H(w) bee transition bands between values on either side of the discontinuity. (ii) The width of the transition bands depends on the width of the main lobe of the frequency response of the window function, w(n) . W(w). (iii) Since the filter frequency response is obtained via a convolution relation , it is clear that the resulting filters are never optimal in any sense. (iv) As M (the length of the window function) increases, the mainlobe width of W(w) is reduced which reduces the width of the transition band, but this also introduces more ripple in the frequency response. (v) The window function eliminates the ringing effects at the bandedge and does result in lower sidelobes at the expense of an increase in the width of the transition band of the filter. Some of the windows [Park87] monly used are as follows: 1. Bartlett triangular window: W(n)=2(n+1)/N+1 n=0,1,2…….,(N1)/2 (9)=22(n+1)/N+1 n=(N1)/2,……,N1= 0 otherwise 2 Generalized cosine windows(Rectangular, Hanning, Hamming and Blackman) W(n)=abcos(2p(n+1)/(N+1))+ccos(4p(n+1)/(N+1)) n=0,1….N1 (10) = 0 otherwise window with parameter β: (11)The general cosine window has four special forms that are monly used. These are determined by the parameters a,b,c TABLE IValue of coefficients