测试技术实验指导书.

1、实验1周期信号波形的合成和分解1实验目的1. 学习使用Matlab，学会用Matlab提供的函数对信号进行频谱分析；2. 加深了解信号分析手段之一的傅立叶变换的基本思想和物理意义；3. 观察和分析由多个频率、幅值和相位成一定关系的正弦波叠加的合成波形；。4. 观察和分析频率、幅值相同，相位角不同的正弦波叠加的合成波形；5. 通过本实验熟悉信号的合成、分解原理，了解信号频谱的含义。2实验原理按富立叶分析的原理，任何周期信号都可以用一组三角函数sin(2ii nf0t)、con(2兀 nf0t)的组合表示oC(n=1 , 2, 3,)x(t)二 a0 (an cos2二 nf0t bn sin2：

2、nf0t)n 4也就是说，我们可以用一组正弦波和余弦波来合成任意形状的周期信号 对于典型的方波，其时域表达式为：-A(-?/2 0)(Qf 1). If x and y are not the same len gth, the shorter vector is zero-padded to the len gth of the Ion ger vector.c=xcorr(x) is the autocorrelation sequence for the vector x.c=xcorr(x,y,maxlags,optio n)where opti on is:biased: Biase

3、d estimate of the cross-correlati on fun cti onun biased: Un biased estimate of the cross-correlati on fun ctio ncoeff: Normalizes the sequence so the autocorrelations at zero lag are identically 1.0 non e, to use the raw, un scaled cross-correlati ons (default) maxlags specifies both x,y a maximum

4、number of lags .Example:求 x1 = sin(2 n 10t)+w(t) 和 x2=w(t)的自相关函数 (w(t)为白噪声)。N=1000; n=0:N-1;Fs=500;t=n/Fs;x1=si n(2*pi*10*t)+0.6*ra ndn (1,le ngth(t);c,lags=xcorr(x1,u nbiased);subplot(2,2,1),plot(t,x1),xlabel(t),ylabel(x1(t),grid;自相关函数),grid;互相关函数),grid;subplot(2,2,2),plot(lags/Fs,c),ylabel(Rxx1(t)

5、, ti tle(x1x2=ra ndn (1,le ngth(t);c,lags=xcorr(x2,u nbiased); subplot(2,2,3),plot(t,x2),xlabel(t),ylabel(x2(t),grid subplot(2,2,4),plot(lags/Fs,c),ylabel(Rxx2(t), ti tle(x2x2互相关函数x1自相关函数ll HL .tJH. J x . - .J|riirni1r i j i q r5. File Openration%We can create a data file:t=0:0.001:0.511;y=si n(2*pi

6、*20*t)+si n(2*pi*70*t)+si n(2*pi*80*t)+si n(2*pi*90*t); save data1 y -ascii; %save y as a text file: data1 x=load(data1); %load file as a variable x% We can create a file as data.txt using any edit :1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3% then use it as a variable , for example:y=load(data.txt); %load

7、file“ data.txt ” as a variable yplot(y);6. Histogram plotn = hist(Y)n = hist(Y,x)DescriptionA histogram shows the distribution of data values.n = hist(Y) bins the elements in Y into 10 equally spaced containers and returns the number of elements in each contain er. If Y is a matrix, hist works dow n

8、 the colu mns.n = hist(Y,x) where x is a vector, returns the distribution of Y among length (x) bins with centers specified by x. For example, if x is a 5-element vector, hist distributes the elements of Y into five bins centered on the x-axis at the eleme nts in x. Note: use histc if it is more n atural to specify bin edges in stead of cen ters.ExampleGen erate a bell-curve histogram from Gaussia n data.x = -2.9:0.129;y = randn (10000,1);hist(y,x)-3450400350300250200150100500-2-101237.功率谱估计pwelch(x,window,noverlap,nfft,fs)x 被估计的信号；windows所加Hanning窗的长度;noverlap被估计信号重叠的长度；nfft fft 的长度；fs采样