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1、-电 子 科 技 大 学实 验 报 告学生：项阳 学 号： 11 指导教师：邓建一、实验工程名称：离散时间傅里叶变换二、实验目的：熟悉序列的傅立叶变换、傅立叶变换的性质、连续信号经理想采样后进展重建，加深对时域采样定理的理解。三、实验容：1. 求以下序列的离散时间傅里叶变换(a) (b) 2. 设画出并观察其周期性。3.设画出并观察其共轭对称性。 4. 验证离散时间傅里叶变换的线性、时移、频移、反转翻褶性质。5. 连续时间信号为，求：(a) 的傅里叶变换；(b) 采样频率为5000Hz，绘出,用理想插函数重建，并对结果进展讨论；(c) 采样频率为1000Hz，绘出，用理想插函数重建，并对结果进
2、展讨论。四、实验原理：1. 离散时间傅里叶变换(DTFT)的定义：2周期性：是周期为的函数3对称性：对于实值序列，是共轭对称函数。4线性：对于任何，有5时移6频移 7反转翻褶五、实验器材设备、元器件：PC机、Windows *P、MatLab 7.1六、实验步骤：本实验要求学生运用MATLAB编程产生一些根本的离散时间信号，并通过MATLAB的几种绘图指令画出这些图形，以加深对相关教学容的理解，同时也通过这些简单的函数练习了MATLAB的使用。七、实验源代码：1aw = 0:1:500*pi/500;* = e*p(j*w) ./ (e*p(j*w) - 0.5*ones(1,501);mag
3、* = abs(*);ang* = angle(*);real* = real(*);imag* = imag(*);subplot(2,2,1);plot(w/pi,mag*);grid*label(frequency in pi units);title(Magnitude Part);ylabel(Magnitude)subplot(2,2,3);plot(w/pi,ang*);grid*label(frequency in pi units);title(Angle Part);ylabel(Radians)subplot(2,2,2);plot(w/pi,real*);grid*la
4、bel(frequency in pi units);title(Real Part);ylabel(Real)subplot(2,2,4);plot(w/pi,imag*);grid*label(frequency in pi units);title(Imaginary Part);ylabel(Imaginary)1.bn = -1:3;* = 1:5;k = 0:500;w = (pi/500)*k;* = * * (e*p(-j*pi/500) . (n*k);mag* = abs(*);ang* = angle(*);real* = real(*);imag* = imag(*);
5、subplot(2,2,1);plot(k/500,mag*);grid*label(frequency in pi units);title(magnitude Part)subplot(2,2,3);plot(k/500,ang*);grid*label(frequency in pi units);title(Angle Part)subplot(2,2,2);plot(k/500,real*);grid*label(frequency in pi units);title(Real Part)subplot(2,2,4);plot(k/500,imag*);grid*label(fre
6、quency in pi units);title(Imaginary Part)2n = 0:10; * = (0.9*e*p(j*pi/3).n;k = -200:200;w = (pi/100)*k;* = * * (e*p(-j*pi/100) . (n*k);mag* = abs(*);ang* = angle(*);subplot(2,1,1);plot(w/pi,mag*);grid*label(frequency in units of pi);ylabel(|*|)title(Magnitude Part)subplot(2,1,2);plot(w/pi,ang*/pi);g
7、rid*label(frequency in units of pi);ylabel(radians/pi)title(Angle Part)3subplot(1,1,1)n = -5:5; * = (-0.9).n;k = -200:200;w = (pi/100)*k;* = * * (e*p(-j*pi/100) . (n*k);mag* = abs(*);ang* = angle(*);subplot(2,1,1);plot(w/pi,mag*);grida*is(-2,2,0,15)*label(frequency in units of pi);ylabel(|*|)title(M
8、agnitude Part)subplot(2,1,2);plot(w/pi,ang*/pi);grida*is(-2,2,-1,1)*label(frequency in units of pi);ylabel(radians/pi)title(Angle Part)41*1 = rand(1,11);*2 = rand(1,11);n = 0:10;alpha = 2; beta = 3;k = 0:500;w = (pi/500)*k;*1 = *1 * (e*p(-j*pi/500).(n*k);*2 = *2 * (e*p(-j*pi/500).(n*k);* = alpha*1 +
9、 beta*2;* = * * (e*p(-j*pi/500).(n*k);*_check = alpha*1 + beta*2;error = ma*(abs(* - *_check)4.2* = rand(1,11);n = 0:10;k = 0:500;w = (pi/500)*k;* = * * (e*p(-j*pi/500).(n*k);y = *; m = n+2;Y = y * (e*p(-j*pi/500).(m*k);Y_check = (e*p(-j*2).w).*;error = ma*(abs(Y - Y_check)4.3n = 0:100; * = cos(pi*n
10、/2);k = -100:100;w = (pi/100)*k;* = * * (e*p(-j*pi/100) . (n*k);y = e*p(j*pi*n/4).*;Y = y * (e*p(-j*pi/100) . (n*k);subplot(1,1,1)subplot(2,2,1);plot(w/pi,abs(*);grid;a*is(-1,1,0,60)*label(frequency in units of pi);ylabel(|*|)title(Magnitude of *)subplot(2,2,2);plot(w/pi,angle(*)/pi);grid;a*is(-1,1,
11、-1,1)*label(frequency in units of pi);ylabel(randiands/pi)title(Angle of *)subplot(2,2,3);plot(w/pi,abs(Y);grid;a*is(-1,1,0,60)*label(frequency in units of pi);ylabel(|Y|)title(Magnitude of Y)subplot(2,2,4);plot(w/pi,angle(Y)/pi);grid;a*is(-1,1,-1,1)*label(frequency in units of pi);ylabel(randiands/
12、pi)title(Angle of Y)4.4n = -5:10; * = rand(1,length(n);k = -100:100;w = (pi/100)*k;* = * * (e*p(-j*pi/100) . (n*k);y = fliplr(*);m = -fliplr(n);Y = y* (e*p(-j*pi/100).(m*k);Y_check = fliplr(*);error = ma*(abs(Y - Y_check)5.aDt = 0.00005; t = -0.005:Dt:0.005;*a = e*p(-1000*abs(t);Wma* = 2*pi*2000;K =
13、500; k = 0:1:K;W = k*Wma*/K;*a = *a * e*p(-j*t*W)*Dt;*a = real(*a);W = -fliplr(W),W(2:501);*a = fliplr(*a),*a(2:501);subplot(1,1,1)subplot(2,1,1);plot(t*1000,*a);*label(t in msec);ylabel(*a(t)title(Analog Signakl)subplot(2,1,2);plot(W/(2*pi*1000),*a*1000);*label(Frequency in KHz);ylabel(*a(jW)*1000)
14、title(Continuous-tine Fouroer Transform)5.bcDt = 0.00005; t = -0.005:Dt:0.005;*a = e*p(-1000*abs(t);Ts = 0.0002;n = -25:1:25;* = e*p(-1000*abs(n*Ts);K =500; k = 0:1:K;w = pi*k/K;* = * * e*p(-j*n*w);* = real(*);w = -fliplr(w),w(2:K+1);* = fliplr(*),*(2:K+1);subplot(1,1,1)subplot(2,1,1);plot(t*1000,*a);*label(t in msec);ylabel(*1(n)title(Discrete Signal);hold onstem(n*Ts*1000,*);gte*t(Ts=0.2 msec);hold offsubplot(2,1,2);plot(w/pi,*);*label(Frequency in pi units);ylabel(*1(w)title(Discrete-time Fourier Transform)八、实验数据及结果分析：2.
