《数字信号处理》Matlab实验

1、数字信号处理Matlab实验 一离散信号的 FFT 分析 1.用Matlab编程上机练习。已知： N=25。这里Q=0.9+j0.3。可以推导出 ， 首先根据这个式子计算X(k)的理论值，然后计算输入序列x(n)的32个值，再利用基2时间抽选的FFT算法，计算x(n)的DFT X(k)，与X(k)的理论值比较（要求计算结果最少6位有效数字）。解：函数代码： function xn() format long q=0.9+0.3*i; wn=exp(-2*pi*i/32); xk=(1-q32)./(1-q*wn.0:31)xn=q.0:31 xk1=fft(xn,32) diff=xk-xk1

2、具体执行情况： function xn()format longq=0.9+0.3*i;wn=exp(-2*pi*i/32);xk=(1-q32)./(1-q*wn.0:31)xk = Columns 1 through 2 0.693972803195698 + 3.499715655993840i 2.792267857648369 + 8.050455721438597i Columns 3 through 4 9.402964607913189 - 9.135013555028673i 1.866445467462052 - 3.833832762635439i Columns 5 t

3、hrough 6 1.131822689478846 - 2.234157347130941i 0.904793922868299 - 1.534629307882413i Columns 7 through 8 0.799557206779214 - 1.139609357830753i 0.739605630813150 - 0.882314367550644i Columns 9 through 10 0.700861643199240 - 0.698565363198060i 0.673575789604202 - 0.558478478082158i Columns 11 throu

4、gh 12 0.653109437428513 - 0.446244996656357i 0.636991253015040 - 0.352689135211701i Columns 13 through 14 0.623788380776217 - 0.272085968296931i 0.612612873742441 - 0.200641851238978i Columns 15 through 16 0.602883340189454 - 0.135703205872800i 0.594200434347139 - 0.075313670713158i Columns 17 throu

5、gh 18 0.586277479436723 - 0.017949220626496i 0.578899608820263 + 0.037651723475093i Columns 19 through 20 0.571898466305671 + 0.092606953506914i 0.565135772013173 + 0.147983310049841i Columns 21 through 22 0.558492135768929 + 0.204880771267792i 0.551859131244066 + 0.264522208758452i Columns 23 throu

6、gh 24 0.545133643745847 + 0.328364940349017i 0.538214362209129 + 0.398257131749283i Columns 25 through 26 0.531001527230573 + 0.476677768575531i 0.523403723684219 + 0.567132338629562i Columns 27 through 28 0.515362483773298 + 0.674849986673143i 0.506925762334513 + 0.808101482252638i Columns 29 throu

7、gh 30 0.498467012317214 + 0.980906313951879i 0.491389377970933 + 1.219207441587793i Columns 31 through 32 0.490732201059483 + 1.577081955159802i 0.517353973624932 + 2.188832884536347i xn=q.0:31xn = Columns 1 through 2 1.000000000000000 0.900000000000000 + 0.300000000000000i Columns 3 through 4 0.720

8、000000000000 + 0.540000000000000i 0.486000000000000 + 0.702000000000000i Columns 5 through 6 0.226800000000000 + 0.777600000000000i -0.029160000000000 + 0.767880000000000i Columns 7 through 8 -0.256608000000000 + 0.682344000000000i -0.435650400000000 + 0.537127200000000i Columns 9 through 10 -0.5532

9、23520000000 + 0.352719360000000i -0.603716976000000 + 0.151480368000000i Columns 11 through 12 -0.588789388800000 - 0.044782761600000i -0.516475621440000 - 0.216941302080000i Columns 13 through 14 -0.399745668672000 - 0.350189858304000i -0.254714144313600 - 0.435094573075200i Columns 15 through 16 -

10、0.098714357959680 - 0.467999359061760i 0.051556885554816 - 0.450813730543488i Columns 17 through 18 0.181645316162381 - 0.390265291822695i 0.280560372092951 - 0.296745167791711i Columns 19 through 20 0.341527885221169 - 0.182902539384655i 0.362245858514449 - 0.062153919879838i Columns 21 through 22

11、0.344667448626955 + 0.052735229662480i 0.294380134865516 + 0.150861941284319i Columns 23 through 24 0.219683538993669 + 0.224089787615542i 0.130488248809639 + 0.267585870552088i Columns 25 through 26 0.037163662763049 + 0.279973758139771i -0.050544830955187 + 0.263125481154709i Columns 27 through 28

12、 -0.124427992206081 + 0.221649483752682i -0.178480038111278 + 0.162156137715589i Columns 29 through 30 -0.209278875614827 + 0.092396512510647i -0.216069941806538 + 0.020373198575134i Columns 31 through 32 -0.200574907198425 - 0.046485103824341i -0.166571885331280 - 0.102009065601434i xk1=fft(xn,32)x

13、k1 = Columns 1 through 2 0.693972803195698 + 3.499715655993839i 2.792267857648366 + 8.050455721438599i Columns 3 through 4 9.402964607913182 - 9.135013555028692i 1.866445467462051 - 3.833832762635439i Columns 5 through 6 1.131822689478845 - 2.234157347130942i 0.904793922868298 - 1.534629307882413i C

14、olumns 7 through 8 0.799557206779213 - 1.139609357830754i 0.739605630813150 - 0.882314367550645i Columns 9 through 10 0.700861643199240 - 0.698565363198060i 0.673575789604202 - 0.558478478082158i Columns 11 through 12 0.653109437428514 - 0.446244996656356i 0.636991253015040 - 0.352689135211701i Colu

15、mns 13 through 14 0.623788380776217 - 0.272085968296931i 0.612612873742441 - 0.200641851238977i Columns 15 through 16 0.602883340189454 - 0.135703205872800i 0.594200434347139 - 0.075313670713159i Columns 17 through 18 0.586277479436723 - 0.017949220626496i 0.578899608820263 + 0.037651723475093i Colu

16、mns 19 through 20 0.571898466305671 + 0.092606953506913i 0.565135772013172 + 0.147983310049840i Columns 21 through 22 0.558492135768929 + 0.204880771267792i 0.551859131244065 + 0.264522208758452i Columns 23 through 24 0.545133643745846 + 0.328364940349016i 0.538214362209129 + 0.398257131749283i Colu

17、mns 25 through 26 0.531001527230572 + 0.476677768575531i 0.523403723684219 + 0.567132338629563i Columns 27 through 28 0.515362483773297 + 0.674849986673144i 0.506925762334512 + 0.808101482252638i Columns 29 through 30 0.498467012317213 + 0.980906313951879i 0.491389377970932 + 1.219207441587793i Colu

18、mns 31 through 32 0.490732201059480 + 1.577081955159802i 0.517353973624928 + 2.188832884536347i diff=xk-xk1diff = 1.0e-013 * Columns 1 through 2 0.001110223024625 + 0.004440892098501i 0.031086244689504 - 0.017763568394003i Columns 3 through 4 0.071054273576010 + 0.195399252334028i 0.015543122344752

19、+ 0.008881784197001i Columns 5 through 6 0.013322676295502 + 0.004440892098501i 0.001110223024625 + 0.004440892098501i Columns 7 through 8 0.006661338147751 + 0.002220446049250i 0 + 0.003330669073875i Columns 9 through 10 0.006661338147751 - 0.001110223024625i 0.005551115123126 - 0.001110223024625i

20、Columns 11 through 12 -0.001110223024625 - 0.005551115123126i 0.001110223024625 + 0.003330669073875i Columns 13 through 14 -0.002220446049250 + 0.001665334536938i 0.003330669073875 - 0.001387778780781i Columns 15 through 16 0.003330669073875 - 0.000277555756156i 0 + 0.002914335439641i Columns 17 thr

21、ough 18 0.002220446049250 - 0.000173472347598i -0.001110223024625 - 0.004302114220422i Columns 19 through 20 0.001110223024625 + 0.002081668171172i 0.001110223024625 + 0.001942890293094i Columns 21 through 22 0.002220446049250 + 0.001110223024625i 0.002220446049250 + 0.000555111512313i Columns 23 th

22、rough 24 0.003330669073875 + 0.002775557561563i 0.003330669073875 - 0.000555111512313i Columns 25 through 26 0.004440892098501 -0.002220446049250 - 0.001110223024625i Columns 27 through 28 0.014432899320127 - 0.006661338147751i 0.008881784197001 - 0.002220446049250i Columns 29 through 30 0.009992007221626 0.013877787807814 - 0.002220446049250i Columns 31 through 32 0.02275957200481