數(shù)字通信原理課件：Lecture2 信號與系統(tǒng)

1、Lecture2 信號與系統(tǒng)本章主要內(nèi)容：q傅里葉級數(shù)仿真q傅里葉變換仿真q功率和能量【什么是傅立葉級數(shù)】n1）周期信號x(t)如果在一個周期內(nèi)可積，則該周期信號可以表示成n2）傅里葉級數(shù)系數(shù)ntnfjnseFtf2)(TTtnfjnndttfTndtetfTFs0020)(10)(1【例2.1 矩形波的傅里葉級數(shù)】n問題：求雙極性周期矩形波的傅立葉級數(shù)并且畫出傅立葉級數(shù)展開后的波形n求解過程：根據(jù)傅立葉級數(shù)的計算公示可得編寫Matlab程序畫出N100時矩形波的近似波形（fb_jinshi.m）2/0)2/(sin0jnnencFF【fb_jinshi.m】給出t的離散取值求出Fn系數(shù)求和項

2、【matlab運行結(jié)果】【思考】n 怎樣讀取數(shù)組中的元素？n怎樣表示求和項？n如果省略 仿真結(jié)果會是怎樣？n自己編寫P4解說題1.1【幅度譜和相位譜】n什么是幅度譜和相位譜？n傅立葉級數(shù) 通常是復數(shù)，它的模 和相位 對n或者nf0作圖，就成為幅 度譜和相位譜nxnxnx【例2、求周期信號的幅度譜和相位譜】e.g.1.3求解過程：1、編寫求解傅立葉系數(shù)的函數(shù)function xx=fseries(funfcn,a,b,n,tol,p1,p2,p3)2、編寫生成周期信號的函數(shù)funfcn3、畫出幅度和相位譜【1、傅里葉級數(shù)系數(shù)的matlab程序】nfunction xx=fseries(funfc

3、n,a,b,n,tol,p1,p2,p3)n%FSERIES Returns the Fourier series coefficients.n% It can depend on up to three parameters p1,p2, and p3. The function is given over one period extending from a to bn% xx=vector of length n+1 of Fourier Seriesn% Coefficients, xx0,xx1,.,xxn.n% p1,p2,p3=parameters of funfcn. n%

4、tol=the error level.【matlab程序】(續(xù)1)n j=sqrt(-1);nargs0=;nfor nn=1:nargin-5n args0=args0,p,int2str(nn);nendnargs=args0,);nt=b-a;nxx(1)=eval(1/(,num2str(t),).*quad(funfcn,a,b,tol,args) ;執(zhí)行命令：1/(t).*quad(funfcn,a,b,tol,p1,p2)nargin=6args0=,p1;nargin=7args0=,p1,p2;args=,p1,p2);【matlab程序】(續(xù)2)nfor i=1:nn n

5、ew_fun = exp_fnct ;n args=, num2str(i), , num2str(t), args0, ) ;nxx(i+1)=eval(1/(,num2str(t),).*quad(new_fun,a,b,tol,funfcn,args);nend執(zhí)行命令： 1/(12).*quad(new_fun,a,b,tol,funfcn,1,12)Matlab命令解釋quadnSyntaxnq = quad(fun,a,b)nq = quad(fun,a,b,tol)nq = quad(fun,a,b,tol,trace)n用途：nQuadrature is a numerical

6、 method used to find the area under the graph of a function, that is, to compute a definite integral.【2、產(chǎn)生高斯函數(shù)的matlab程序】nfunction y=normal(x,m,s)n% FUNCTION y=NORMAL(x,m,s)n% Gaussian distributionn% m=meann% s=standard deviationny=(1/sqrt(2*pi*s2)*exp(-(x-m).2)/(2*s2);【3、matlab主程序Ip_01_03.m】n% MATLA

7、B script for Illustrative Problem 3, Chapter 1.necho onnfnct=normal;na=-6;nb=6;nn=24;ntol=0.1;【matlab程序】(cont.)nxx=fseries(fnct,a,b,n,tol,0,1);nxx1=xx(n+1:-1:2);nxx1=conj(xx1),xx;nabsxx1=abs(xx1);npause % Press any key to see a plot of the magnitude.nn1=-n:n;nstem(n1,absxx1)ntitle(The Discrete Magni

8、tude Spectrum)求雙邊幅度譜畫雙邊幅度譜【matlab程序】(cont.)nphasexx1=angle(xx1);npause % Press any key to see a plot of the phase.nstem(n1,phasexx1)ntitle(The Discrete Phase Spectrum)畫相位譜Matlab命令解釋conjnconj功能：Complex conjugatenSyntax語法：ZC = conj(Z)nDescriptionZC = conj(Z) returns the complex conjugate of the elemen

9、ts of Z.nAlgorithmsIf Z is a complex array:conj(Z) = real(Z) - i*imag(Z)【程序運行結(jié)果】-30-20-10010203000.010.020.030.040.050.060.070.08The Discrete Magnitude Spectrum【程序運行結(jié)果】cont.-30-20-100102030-4-3-2-101234The Discrete Phase Spectrum思考：n自己編寫P8解說題1.2【周期信號的過濾】【解答】編程思路？編程思路？【matlab程序】n% MATLAB script for I

10、llustrative Problem 4, Chapter 1.necho onnn=-20:1:20;n% Fourier series coefficients of x(t) vector nx=.5*(sinc(n/2).2;n% sampling intervalnts=1/40;n% time vectornt=-.5:ts:1.5;n% impulse responsenfs=1/ts;nh=zeros(1,20),t(21:61),zeros(1,20);在時間段01上系統(tǒng)沖擊響應【matlab程序】cont.n% transfer functionnH=fft(h)/fs;

11、n% frequency resolutionndf=fs/80;nf=0:df:fs-fs/2;n% rearrange HnH1=fftshift(H);ny=x.*H1(21:61);n% Plotting commands follow.得到雙邊頻率分量【matlab程序】cont.nfigure (1); % plot nplot(f,abs(H1);nfigure (2);nstem(f,abs(H1);nfigure (3);nstem(f(21:61),abs(y);【命令解釋fft和fftshift】nfft(X) is the discrete Fourier transf

12、orm (DFT) of vector X.nfft(X,N) is the N-point FFT, padded with zeros if X has less than N points and truncated if it has more.nfftshift Shift zero-frequency component to center of spectrum.思考：n如何求非周期函數(shù)的傅立葉變換？n如果得到雙邊頻譜？【程序運行結(jié)果】-20-15-10-50510152000.10.20.30.40.50.60.7【程序運行結(jié)果】（cont.）-20-15-10-5051015

13、2000.10.20.30.40.50.60.7【程序運行結(jié)果】（cont.）-10-5051000.050.10.150.20.250.30.35【傅里葉變換】n什么是傅立葉變換？n傅立葉變換是傅立葉級數(shù)對非周期信號的推廣n信號的傅立葉變換成為信號的頻譜，一般是個復函數(shù)，幅度譜和相位譜為：dfefXtxdtetxfXftjftj22)()()()(fXfX例5：求非周期信號的幅度和相位譜思路：思路：1、非周期信號離散化、非周期信號離散化 2、用、用DFT變換變換 3、再轉(zhuǎn)變、再轉(zhuǎn)變成模擬周期信號的傅立葉變換成模擬周期信號的傅立葉變換【子程序】nfunction M,m,df=fftseq(m

14、,ts,df) n% M,m,df=fftseq(m,ts,df)n% M,m,df=fftseq(m,ts)n%FFTSEQ generates M, the FFT of the sequence m.n% The sequence is zero padded to meet the required frequency resolution df.n% ts is the sampling interval. The output df is the final frequency resolution.n% Output m is the zero padded version of

15、 input m. 【子程序】cont.nfs=1/ts;nif nargin = 2n n1=0;nelsen n1=fs/df;nendnn2=length(m);nn=2(max(nextpow2(n1),nextpow2(n2);nM=fft(m,n);nm=m,zeros(1,n-n2);ndf=fs/n;Matlab命令解釋nnextpow2n語法：p = nextpow2(A)nDescriptionnp = nextpow2(A) returns the smallest power of two that is greater than or equal to the abs

16、olute value of A. (That is, p that satisfies 2p = abs(A).nThis function is useful for optimizing FFT operations, which are most efficient when sequence length is an exact power of two.Matlab命令解釋 （cont.）nExamplesnFor any integer n in the range from 513 to 1024, nextpow2(n) is 10.nFor vector input, ne

17、xtpow2(n) returns an element-by-element result:nA = 1 2 3 4 5 9 519nnextpow2(A)nans =n 0 1 2 2 3 4 10【matlab程序】n% MATLAB script for Illustrative Problem 1. 5.ndf=0.01;nfs=10;nts=1/fs;nt=-5:ts:5;nx1=zeros(size(t);nx1(41:51)=t(41:51)+1;nx1(52:61)=ones(size(x1(52:61); %x1(t)【matlab程序】cont.nx2=zeros(size(t);nx2(51:71)=x1(41:61); %x2(t)nX1,x11,df1=fftseq(x1,ts,df);nX2,x21,df2=fftseq(x2,ts,df);nX11=X1/fs;nX21=X2/fs;nf=0:df1:df1*(length(x11)-1)-fs/2;【matlab程序】cont.nplot(f