DSP实验一 信号及系统响应的谱分析，南京理工大学紫金学院实验报告

7256205154310251002468002468

73.525632052.5154231.51021510.50024002400510

分析：

c) 程序内容：（包括主程序和子程序dft.m）

function xk=dft(xn)

N=length(xn); n=0:N-1;k=0:N-1;

xk=(xn)*exp(-j*2*pi/N).^(n'*k);

tic; n=0:3;

xn=[1 0 2 4]; xk=dft(xn); k=0:3;

hn=power(0.9,n); hk=dft(hn); y=conv(xn,hn); yk=dft(y); toc;

Elapsed time is 0.063000 seconds.

subplot(1,2,1);stem(n,xn)

subplot(1,2,2);stem(n,abs(xk)) figure(2);

subplot(1,2,1);stem(n,hn) subplot(1,2,2);stem(k,abs(hk)) figure(3);

subplot(1,2,1);stem(y)

subplot(1,2,2);stem(abs(yk)) figure(4);

subplot(1,3,1);stem(abs(xk)) subplot(1,3,2);stem(abs(hk)) subplot(1,3,3);stem(abs(yk))

d) xk =

7.0000 -1.0000 + 4.0000i -1.0000 - 0.0000i -1.0000 - 4.0000i hk =

3.4390 0.1900 - 0.1710i 0.1810 - 0.0000i 0.1900 + 0.1710i y =

1.0000 0.9000 2.8100 6.5290 5.2200 4.6980 2.9160 yk =

24.0730 -8.8769 + 2.8489i 0.7118 + 2.1697i -0.3713 - 1.8776i + 1.8776i 0.7118 - 2.1697i -8.8769 - 2.8489i

Elapsed time is 0.032000 seconds.

-0.3713 运行时间t1= 0.032000 seconds

2）利用FFT实现线性卷积计算

a) yn = Columns 1 through 5

1.5550 1.5684 + 0.0638i 1.5046 + 0.1146i 1.4198 + 0.0847i 1.3995

Columns 6 through 10

1.4532 - 0.0513i 1.5046 - 0.0273i 1.4877 + 0.0168i 1.4315 1.4247 - 0.0798i

Columns 11 through 15

1.5046 - 0.1373i 1.6053 - 0.1007i 1.6323 1.5719 + 0.0673i 1.5046 + 0.0499i

Column 16 1.5054 - 0.0009i

b) xk= 7.0000 -1.0000 + 4.0000i -1.0000 -1.0000 - 4.0000i

hk=3.4390 0.1900 - 0.1710i 0.1810 0.1900 + 0.1710i yk= 24.0730 0.4940 + 0.9310i -0.1810 0.4940 - 0.9310i

按要求给出相关的图形

43.532.54231.510.5027651012300123

10.90.80.70.60.50.40.30.20.1001230.150.10.050-0.05-0.1-0.15-0.2051015203.532.521.510.50012325201510501234