【文章內(nèi)容簡(jiǎn)介】 的效果符合設(shè)計(jì)要求。 優(yōu)化設(shè)計(jì)的Matlab實(shí)現(xiàn)在優(yōu)化設(shè)計(jì)的Matlab實(shí)現(xiàn)中，程序中經(jīng)常使用remez函數(shù)，這種函數(shù)的使用方法為： b=remez(n,f,a,w,’ftype’)①n為待設(shè)計(jì)濾波器的階數(shù)；f是一個(gè)向量，它是一個(gè)0到1的正數(shù)②a是一個(gè)向量，指定頻率段的幅度值；w對(duì)應(yīng)于各個(gè)頻段的加權(quán)值③函數(shù)的返回值b是設(shè)計(jì)出的濾波器的系數(shù)組成的一個(gè)長(zhǎng)度為n+1的向量(1) 利用Remez函數(shù)設(shè)計(jì)等波紋低通濾波器設(shè)計(jì)要求：①， , 采樣頻率2000Hz②阻帶衰減大于等于40dB，程序參見(jiàn)附錄二中的3（1）利用Remez函數(shù)設(shè)計(jì)等波紋低通濾波器圖416 等波紋低通濾波器的增益響應(yīng)從參考程序及圖416可以得到所設(shè)計(jì)出濾波器的參數(shù)如下：①濾波器的采樣頻率為2000Hz，濾波器的階數(shù)為22②，③阻帶衰減為40dB，對(duì)比設(shè)計(jì)要求與所設(shè)計(jì)出濾波器的參數(shù)可知，其各項(xiàng)參數(shù)均滿(mǎn)足設(shè)計(jì)指標(biāo)，所設(shè)計(jì)出的濾波器即為設(shè)計(jì)所要求的濾波器。圖417 信號(hào)濾波前的時(shí)域圖和頻域圖圖418 信號(hào)濾波后的時(shí)域圖和頻域圖從圖417和圖418的圖像中可以看到：輸入信號(hào)是由兩個(gè)不同頻率的正弦信號(hào)疊加而成，信號(hào)頻域圖中位于濾波器通帶內(nèi)的頻率分量保留了下來(lái)，位于濾波器阻帶內(nèi)的頻率分量被濾除，濾波器的效果符合設(shè)計(jì)要求。(2) 利用Remez函數(shù)設(shè)計(jì)等波紋帶通濾波器設(shè)計(jì)要求：①、 ②阻帶衰減大于等于40dB③④采樣頻率2000Hz程序參見(jiàn)附錄二中的3（2）利用Remez函數(shù)設(shè)計(jì)等波紋帶通濾波器圖419 等波紋帶通濾波器的增益響應(yīng)從參考程序及圖419可以得到所設(shè)計(jì)出濾波器的參數(shù)如下：①濾波器的采樣頻率為2000Hz，濾波器的階數(shù)為22②、③阻帶衰減為40dB，對(duì)比設(shè)計(jì)要求與所設(shè)計(jì)出濾波器的參數(shù)可知，其各項(xiàng)參數(shù)均滿(mǎn)足設(shè)計(jì)指標(biāo)，所設(shè)計(jì)出的濾波器即為設(shè)計(jì)所要求的濾波器。圖420 信號(hào)濾波前的時(shí)域圖和頻域圖圖421 信號(hào)濾波后的時(shí)域圖和頻域圖從圖420和圖421的圖像中可以看到：輸入信號(hào)是由四個(gè)不同頻率的正弦信號(hào)疊加而成，信號(hào)頻域圖中位于濾波器通帶內(nèi)的頻率分量保留了下來(lái)，位于濾波器阻帶內(nèi)的頻率分量被濾除，濾波器的效果符合設(shè)計(jì)要求。(3) 利用Remez函數(shù)設(shè)計(jì)等波紋帶阻濾波器設(shè)計(jì)要求：①、 ②阻帶衰減大于等于15dB③④采樣頻率2000Hz 程序參見(jiàn)附錄二中的3（3）利用Remez函數(shù)設(shè)計(jì)等波紋帶阻濾波器圖422 等波紋帶阻濾波器的增益響應(yīng)從參考程序及圖422可以得到所設(shè)計(jì)出濾波器的參數(shù)如下：①濾波器的采樣頻率為2000Hz，濾波器的階數(shù)為22②、③阻帶衰減為15dB，對(duì)比設(shè)計(jì)要求與所設(shè)計(jì)出濾波器的參數(shù)可知，其各項(xiàng)參數(shù)均滿(mǎn)足設(shè)計(jì)指標(biāo)，所設(shè)計(jì)出的濾波器即為設(shè)計(jì)所要求的濾波器。圖423 信號(hào)濾波前的時(shí)域圖和頻域圖圖424 信號(hào)濾波后的時(shí)域圖和頻域圖從圖423和圖424的圖像中可以看到：輸入信號(hào)是由四個(gè)不同頻率的正弦信號(hào)疊加而成，信號(hào)頻域圖中位于濾波器通帶內(nèi)的頻率分量保留了下來(lái)，位于濾波器阻帶內(nèi)的頻率分量被濾除，濾波器的效果符合設(shè)計(jì)要求。 利用濾波器處理加有噪聲的音頻波形（1） 利用窗函數(shù)法設(shè)計(jì)的低通濾波器處理加有噪聲的音頻波形程序參見(jiàn)附錄二4（1）利用窗函數(shù)法設(shè)計(jì)的低通濾波器處理加噪聲的音頻波形圖425 加噪前錄音波形的時(shí)域圖和頻域圖圖426 加噪后錄音波形的時(shí)域圖和頻域圖圖427 窗函數(shù)法設(shè)計(jì)低通濾波器的增益響應(yīng)圖428 濾波后錄音波形的時(shí)域圖和頻域圖從參考程序及以上的四個(gè)圖像中可以得到如下結(jié)論：①?gòu)匿浺舨ㄐ蔚念l域圖可以看到其頻率分量主要在0到6000Hz之間，噪聲的頻率分量主要集中在7000Hz，利用通帶截頻為6000Hz的低通濾波器可以濾除噪聲。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266③，④，阻帶衰減約為53dB（2） 利用優(yōu)化設(shè)計(jì)的低通濾波器處理加有噪聲的音頻波形程序參見(jiàn)附錄二中4（2）利用優(yōu)化設(shè)計(jì)的低通濾波器處理加有噪聲的音頻波形圖429 加噪前錄音波形的時(shí)域圖和頻域圖圖430 加噪后錄音波形的時(shí)域圖和頻域圖圖431 等波紋低通濾波器的增益響應(yīng)圖432 濾波后錄音波形的時(shí)域圖和頻域圖從參考程序及以上的四個(gè)圖像中可以得到如下結(jié)論：①?gòu)匿浺舨ㄐ蔚念l域圖可以看到其頻率分量主要在0到6000Hz之間，噪聲的頻率分量主要集中在7000Hz，利用通帶截頻為6000Hz的低通濾波器可以濾除噪聲。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