1、Northeastern UniversityThe College of Information Science and Engineering現(xiàn)代信號(hào)處理新方法 班級(jí)：電子1201班 姓名：劉悅 學(xué)號(hào)：20123662Northeastern UniversityThe College of Information Science and Engineering 題目一 模擬隨機(jī)試驗(yàn)計(jì)算圓周率pi 題目二 窗函數(shù)法設(shè)計(jì)FIR數(shù)字濾波器 題目四 數(shù)字濾波器過濾高斯白噪聲 主要內(nèi)容主要內(nèi)容Northeastern UniversityThe College of Information Sci

2、ence and Engineering題目一 用計(jì)算機(jī)模擬蒲豐投針的實(shí)驗(yàn)，并估計(jì)隨機(jī)事件發(fā)生的概率以計(jì)算圓周率pi。投擲n次相交次數(shù)為m平行線的距離為a針長(zhǎng)度為l相交概率p=m/n=2l/(a* ) =2l/(a*p)Northeastern UniversityThe College of Information Science and EngineeringNortheastern UniversityThe College of Information Science and Engineeringmatlab實(shí)現(xiàn)方法a=1; %設(shè)置兩條平行線之間的距離I=0.6; %投針的長(zhǎng)度m=0

3、; %針與平行線相交的次數(shù)n=10000000; %投擲次數(shù)x=unifrnd(0,a/2,1,n); %產(chǎn)生n個(gè)(0,a/2)之間均勻分布的隨機(jī)數(shù)phi=unifrnd(0,pi,1,n); %產(chǎn)生n個(gè)(0,pi)之間均勻分布的隨機(jī)數(shù)，這里pi是投針到最近的平行線的角度for i=1:n if x(i)I*sin(phi(i)/2 %只要x小于I*sin(phi(i)/2,則相交 m=m+1; %相交次數(shù)加1 endendfrequency=m/n; %計(jì)算相交的頻率，即相交次數(shù)比總次數(shù)pi=2*I/(a*frequency) %從相交的頻率求總的piNortheastern Univers

4、ityThe College of Information Science and Engineering試驗(yàn)次數(shù)：10000000試驗(yàn)次數(shù)：1000000試驗(yàn)次數(shù)：100000Northeastern UniversityThe College of Information Science and Engineering 窗函數(shù)法窗函數(shù)法 濾波器特性圖 處理疊加的正弦信號(hào),使信號(hào)通過濾波器后留下指定頻率 處理加噪聲的語音信號(hào)，過濾噪聲，得到清晰的語音信號(hào)題目二 FIR數(shù)字濾波器設(shè)計(jì)Northeastern UniversityThe College of Information Scienc

5、e and Engineering低通濾波器通帶截止頻率：200HZ，阻帶起始頻率：300HZ采樣頻率fs=2000HZ階數(shù)m=66最小阻帶衰減-50db（海明窗） 濾波器指標(biāo)N6 . 6sstp2Northeastern UniversityThe College of Information Science and Engineering 設(shè)計(jì)過程 FIR濾波器的窗函數(shù)法設(shè)計(jì)過程：)()n()n()(H)n( jDTFTxdIDTFTjdeHhhe)(jdeH是逼近的理想濾波器頻率響應(yīng)，)(hdk是理想濾波器的單位脈沖響應(yīng))()sincnncc（)n(dh21MjjdeeH)(cc-Nor

6、theastern UniversityThe College of Information Science and EngineeringM=66;fp=200;fst=300;fc=250;fs=2000;wc=2*pi*fc/fs; %將模擬濾波器的技術(shù)指標(biāo)轉(zhuǎn)換為數(shù)字濾 波器技術(shù)指標(biāo)alpha=(M-1)/2;n=0:1:(M-1);m=n-alpha;hd=sin(wc*m)./(pi*m); %hd為理想沖激相應(yīng)w_ham=(hamming(M); %漢明窗h=hd.*w_ham; %加窗H,w=freqz(h,1); %求頻譜mag=abs(H); %求實(shí)部db=20*log(ma

7、g); %衰減Northeastern UniversityThe College of Information Science and Engineeringsubplot(221);stem(hd);title(理想沖擊響應(yīng));axis(0 M-1 -0.1 0.3);ylabel(hdn);subplot(222);stem(w_ham);title(海明窗);axis(0 M-1 0 1.1);ylabel(wn);subplot(223);stem(h);title(實(shí)際沖擊響應(yīng));axis(0 M-1 -0.1 0.3);ylabel(hn);subplot(224);plot(w

8、/(2*pi),db);title(衰減幅度);ylabel(Hw);Northeastern UniversityThe College of Information Science and Engineering0204060-0.100.10.20.3理 想 沖 擊 響 應(yīng)hdn020406000.51海 明 窗wn0204060-0.100.10.20.3實(shí) 際 沖 擊 響 應(yīng)hn05001000-300-200-1000100衰 減 幅 度HwNortheastern UniversityThe College of Information Science and Engineeri

9、ng頻率分別為：150HZ，300HZ，700HZ采樣頻率fs=2000HZ正弦信號(hào)Northeastern UniversityThe College of Information Science and Engineeringf1=150;f2=300;f3=700; %待濾波正弦信號(hào)頻率fs=2000; %采樣頻率subplot(211);t=0:1/fs:0.25; %定義時(shí)間范圍和步長(zhǎng)s=sin(2*pi*f1*t)+sin(2*pi*f2*t)+sin(2*pi*f3*t);%濾波前信號(hào)plot(t,s); %濾波前的信號(hào)圖像xlabel(時(shí)間/秒);ylabel(幅度);titl

10、e(信號(hào)濾波前時(shí)域圖);subplot(212);Fs=fft(s,512); %將信號(hào)變換到頻域AFs=abs(Fs); %信號(hào)頻域圖的幅值f=(0:255)*fs/512; %頻率采樣plot(f,AFs(1:256); %濾波前的信號(hào)頻域圖xlabel(頻率/赫茲);ylabel(幅度);title(信號(hào)濾波前頻域圖);Northeastern UniversityThe College of Information Science and Engineering00.050.10.150.20.25-4-2024時(shí) 間 /秒幅度信 號(hào) 濾 波 前 時(shí) 域 圖01002003004005

11、0060070080090010000100200300頻 率 /赫 茲幅度信 號(hào) 濾 波 前 頻 域 圖即將被過濾頻率的信號(hào)Northeastern UniversityThe College of Information Science and Engineeringsf=filter(h,1,s);%使用filter函數(shù)對(duì)信號(hào)進(jìn)行濾波subplot(211);plot(t,sf);%濾波后的信號(hào)圖像xlabel(時(shí)間/秒);ylabel(幅度);title(信號(hào)濾波后時(shí)域圖);axis(0.2 0.25 -2 2);%限定圖像坐標(biāo)范圍subplot(212);Fsf=fft(sf,512

12、);%濾波后的信號(hào)頻域圖AFsf=abs(Fsf);%信號(hào)頻域圖的幅值f=(0:255)*fs/512;%頻率采樣plot(f,AFsf(1:256)%濾波后的信號(hào)頻域圖xlabel(頻率/赫茲); ylabel(幅度);title(信號(hào)濾波后頻域圖); Northeastern UniversityThe College of Information Science and Engineering0.20.2050.210.2150.220.2250.230.2350.240.2450.25-2-1012時(shí) 間 /秒幅度信 號(hào) 濾 波 后 時(shí) 域 圖010020030040050060070

13、08009001000050100150200頻 率 /赫 茲幅度信 號(hào) 濾 波 后 頻 域 圖保留150HZ頻率信號(hào)Northeastern UniversityThe College of Information Science and Engineering過濾語音信號(hào) 錄制一段語音信號(hào)，頻率在300HZ3.4kHZ范圍內(nèi) 噪聲是10kHZ的正弦信號(hào) 濾波器的截止頻率是4kHZNortheastern UniversityThe College of Information Science and Engineeringf4=10000;%所加噪聲正弦函數(shù)的頻率Y,fs,bits=wav

14、read(F:b.wav);%利用wavread產(chǎn)生音頻的函數(shù)及采樣頻率L=length(Y);t=0:1/fs:(L-1)/fs;%定義時(shí)間的范圍及步長(zhǎng)f=0:fs/L:fs*(L-1)/L;subplot(211);plot(t,Y);xlabel(時(shí)間(t);ylabel(幅度(Y);title(加噪前音頻語音波形的時(shí)域圖);y=0.05*sin(2*pi*f4*t);Y=Y(:,1);%取Y矩陣的第一列Y1=y+Y;%給音頻加噪聲subplot(212);plot(t,Y1);xlabel(時(shí)間(t);ylabel(幅度(Y);title(加噪后音頻語音波形的時(shí)域圖);Northeas

15、tern UniversityThe College of Information Science and EngineeringFY=abs(fft(Y,L);%原始音頻信號(hào)的傅里葉變換subplot(211)plot(f,FY); grid on;%加噪前音頻的頻域圖xlabel(頻率(f);ylabel(幅度(FY);title(加噪前音頻波形的頻域圖);FY1=abs(fft(Y1,L);%加噪聲的傅里葉變換subplot(212)plot(f,FY1);grid on;%加噪后音頻的頻域圖xlabel(頻率(f);ylabel(幅度(FY1);title(加噪聲后音頻波形的頻域圖);

16、Northeastern UniversityThe College of Information Science and Engineering024681012-1-0.500.51024681012-1-0.500.51時(shí) 間 (t)幅度(Y)加 噪 后 音 頻 語 音 波 形 的 時(shí) 域 圖Northeastern UniversityThe College of Information Science and Engineering00.511.522.533.544.5x 10401000200030004000頻 率 (f)幅度(FY)加 噪 前 音 頻 波 形 的 頻 域 圖0

17、0.511.522.533.544.5x 10401000200030004000頻 率 (f)幅度(FY1)加 噪 聲 后 音 頻 波 形 的 頻 域 圖Northeastern UniversityThe College of Information Science and EngineeringM=66;fc=2000;fst=3000;wc=2*pi*fc/fs;%參數(shù)轉(zhuǎn)換，將模擬濾波器的技術(shù)指標(biāo)轉(zhuǎn)換為數(shù)字濾波器的技術(shù)指標(biāo)alpha=(M-1)/2;n=0:1:(M-1)m=n-alpha;hd=sin(wc*m)./(pi*m);%hd為理想沖激相應(yīng)w_ham=(hamming(M)

18、;%漢寧窗（轉(zhuǎn)置矩陣）h=hd.*w_ham;%加窗H,w=freqz(h,1,1000,whole);%求頻譜mag=abs(H);%求實(shí)部db=20*log(mag);%衰減Northeastern UniversityThe College of Information Science and Engineeringsf=filter(h,1,Y1);%使用filter函數(shù)對(duì)信號(hào)進(jìn)行濾波subplot(211);plot(t,sf);%濾波后的信號(hào)圖像xlabel(時(shí)間/秒);ylabel(幅度);title(信號(hào)濾波后時(shí)域圖);subplot(212);Fsf=fft(sf,L);%濾

19、波后的信號(hào)頻域圖AFsf=abs(Fsf);%信號(hào)頻域圖的幅值plot(f,AFsf)%濾波后的信號(hào)頻域圖xlabel(頻率/赫茲); ylabel(幅度);title(信號(hào)濾波后頻域圖); sound(sf,fs);wavwrite(sf,fs,F:hao);wavwrite(Y1,fs,F:noise);Northeastern UniversityThe College of Information Science and Engineering024681012-1-0.500.51時(shí) 間 /秒幅度信 號(hào) 濾 波 后 時(shí) 域 圖00.511.522.533.544.5x 1040100

20、0200030004000頻 率 /赫 茲幅度信 號(hào) 濾 波 后 頻 域 圖Northeastern UniversityThe College of Information Science and Engineering題目四 編寫MATLAB程序，計(jì)算在 的加性高斯白噪聲環(huán)境下，幅度為0.3，頻率為10Hz的正弦信號(hào)通過50Hz低通濾波器的情況。 編寫功率譜為 的加性高斯白噪聲 疊加到正弦信號(hào)上 加噪信號(hào)通過濾波器5-0101N5-101Northeastern UniversityThe College of Information Science and Engineering實(shí)現(xiàn)高斯

21、白噪聲環(huán)境下的正弦信號(hào)fs=1000;fc=10;t=(0:1/fs:1);y1=0.3*sin(2*pi*fc*t);y2=wgn(1,length(y1),5*10-6,dBm);%生成高斯白噪聲y=y1+y2;figure(1);subplot(211);plot(y2);subplot(212);plot(y);grid on;Northeastern UniversityThe College of Information Science and Engineering020040060080010001200-0.2-0.100.10.2高 斯 白 噪 聲020040060080010001200-0.500.5疊 加 信 號(hào)Northeastern UniversityThe College of Information Science and Engineering50HZ低通濾波