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1、问题1：试生成一个含噪声信号，利用matlab中的小波去噪和小波包去噪函数去除噪声，比较两者的性能差异。程序如下：clcclearallloadnoisdoppx=noisdopp;subplot(311)plot(x);title(原始信号的波形图)axistight;thr,sorh,keepapp=ddencmp(den,wv,x);xwd=wden(x,rigrsure,s,one,4,sym4);subplot(312)plot(xwd)title(小波降噪信号)axistightthr1,sorh1,keepapp1,crit=ddencmp(den,wp,x);xwpd=wpde
2、ncmp(x,h,4,sym4,sure,thr1,1);subplot(313)plot(xwpd)title(小波包降噪信号)axistight运行结果如下：原始信号的波形图50-51002003004005006007008009001000小波降噪信号10020030040050060070080090010001002003004005006007008009001000小波包降噪信号50-550-5区别：小波变换在低信噪比情况下的去噪效果较好，小波包分解去噪后信号更加的平滑；小波分解主要是针对细节成分全置0或者给定软（硬）阈值去噪，容易丢失信号中的有用信息。问题2：研究小波包分解树
3、中各节点的重构系数，给出其频谱分布讨论波包分解的频带划分程序如下：clcclearallloadnoisdopp;s=noisdopp;wpt=wpdec(s,3,sym1);plot(wpt);r20=wprcoef(wpt,20);subplot(621)plot(r20)title(r20)subplot(623)hua_fft(r20,10000,1)title(r20的FFT)r21=wprcoef(wpt,21);subplot(622)plot(r21)title(r21)subplot(624)hua_fft(r21,10000,1)title(r21的FFT)r22=wprc
4、oef(wpt,22);subplot(625)plot(r22)title(r22)subplot(627)hua_fft(r22,10000,1)title(r22的FFT)r23=wprcoef(wpt,23);subplot(626)plot(r23)title(r23)subplot(628)hua_fft(r23,10000,1)title(r23的FFT)r10=wprcoef(wpt,10);subplot(629)plot(r10)title(r10)subplot(6,2,11)hua_fft(rl0,10000,l)title(rlO的FFT)r11=wprcoef(wp
5、t,11);subplot(6,2,10)plot(r11)title(r11)subplot(6,2,12)hua_fft(r11,10000,1)title(r11的FFT)程序运行结果如下：TreeDecomposition(0,0)(1,0)(1,1)(2,0)(2,1)(2,2)(2,3)(3,0)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(3,7)datafornode:(0)or(0,0).1086420-2-4-6-8-102004006008001000r20的FFT斗2r215i0林*柯岬哼朴啼i*“N-5一50010001500證1的FFT0.2,010
6、002000300040005000-.一”，显叫a胡訥帽刪榊心也辰r22的FFTrlOFFT411112o01W02000300040005000寸刪4010002000300040005000r11问题3：生成最优树结构，给出其熵值程序如下：clcclearallloadnoisdopp;x=noisdopp;wpt=wpdec(x,3,sym4);wpt=wpsplt(wpt,30);plot(wpt)bt=besttree(wpt);plot(bt)ent=read(wpt,ent,allnodes(wpt)T=entrupd(bt,shannon);ent=read(wpt,ent,
7、allnodes(bt)图1TreeDecomposition1086420-2-4-6-8-10小波包树1086420-2-4-6-8-102004006008001000datafornode:(0)or(0,0).2004006008001000图2最优小波包树表1小波包树中各节点的熵值0010112021222330-3.3195-3.8687-0.0128-4.4528-0.0194-0.0068-0.0071-5.03453233343536374041-0.0041-0.0374-0.0033-0.0026-0.0049-0.0014-5.3961-0.227031-0.0406表2最优小波包树中各节点的熵值001011202122233031-3.3195-3.8687-0.0128-4.4528-0.0194-0.0068-0.0071-5.0345-0.040632334041-0.0041-0.0374-5.3961-0.2270
