2.1clcclose all;n=0:15;p=8;q=2;x=exp(-(n-p.^2/q;figure(1;subplot(3,1,1;stem(n,x;title('exp(-(n-p^2/q,p=8,q=2'; xk1=fft(x,16;q=4;x=exp(-(n-p.^2/q;subplot(3,1,2;xk2=fft(x,16;stem(n,x;title('exp(-(n-p^2/q,p=8,q=4'; q=8;x=exp(-(n-p.^2/q;xk3=fft(x,16;subplot(3,1,3;stem(n,x;title('exp(-(n-p^2/q,p=8,q=8';%时域特性figure(2;subplot(3,1,1;stem(n,abs(xk1;title('exp(-(n-p^2/q,p=8,q=2';subplot(3,1,2;stem(n,abs(xk2;title('exp(-(n-p^2/q,p=8,q=4';subplot(3,1,3;stem(n,abs(xk3;title('exp(-(n-p^2/q,p=8,q=8';%频域特性%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%p=8;q=8;figure(3;subplot(3,1,1;stem(n,x;title('exp(-(n-p^2/q,p=8,q=8';xk1=fft(x,16;p=13;x=exp(-(n-p.^2/q;subplot(3,1,2; xk2=fft(x,16;stem(n,x;title('exp(-(n-p^2/q,p=13,q=8';p=14;x=exp(-(n-p.^2/q;xk3=fft(x,16;subplot(3,1,3;stem(n,x;title('exp(-(n-p^2/q,p=14,q=8';%时域特性figure(4; subplot(3,1,1;stem(n,abs(xk1;title('exp(-(n-p^2/q,p=8,q=8';subplot(3,1,2;stem(n,abs(xk2;title('exp(-(n-p^2/q,p=13,q=8';subplot(3,1,3;stem(n,abs(xk3;title('exp(-(n-p^2/q,p=14,q=8';%频域特性2.2 clcclose alln=0:15;f=0.0625;a=0.1;xb1=exp(-a*n.*sin(2*pi*f*n;xk1=fft(xb1,16;f=0.4375;xb2=exp(-a*n.*sin(2*pi*f*n;xk2=fft(xb2,16;f=0.5625;xb3=exp(-a*n.*sin(2*pi*f*n;xk3=fft(xb3,16;figure(1;subplot(3,1,1;stem(n,xb1;title('f=0.0625';subplot(3,1,2;stem(n,xb2; title('f=0.4375'; subplot(3,1,3; stem(n,xb3; title('f=0.5625'; figure(2; subplot(3,1,1; stem(n,abs(xk1; title('f=0.0625'; subplot(3,1,2; stem(n,abs(xk2; title('f=0.4375'; subplot(3,1,3; stem(n,abs(xk3; title('f=0.5625';2.3clcclose all;N=8;n=0:N-1;xc=0:7;xd=0:7;for m=0:7;if(0<=m & m<=3xc(m+1=m;xd(m+1=4-m;elseif(4<=m & m<=7 xc(m+1=8-m;xd(m+1=m-4;endendfigure(1;subplot(2,1,1;stem(n,xc;title('三角波序列'; subplot(2,1,2;stem(n,xd;title('反三角波序列';xck=fft(xc,N;xdk=fft(xd,N;figure(2;subplot(2,1,1;stem(n,abs(xck;title('三角波序列8点fft'; subplot(2,1,2; stem(n,abs(xdk;title('反三角波序列8点fft'; figure(3; xck1=fft(xc,32;xdk1=fft(xd,32;subplot(2,1,1; stem(0:4*N-1,abs(xck1; title('三角波序列32点fft';subplot(2,1,2;stem(0:4*N-1,abs(xdk1;title('反三角波序列32点fft';2.4clcclose allN=16;detaf=1/16;n=0:N-1;x=sin(2*pi*0.125*n+cos(2*pi*(0.125+detaf *n; xk=fft(x,N;figure(1;subplot(2,1,1;stem(n,abs(xk;title('N=16,Δf=1/16';detaf=1/64;x=sin(2*pi*0.125*n+cos(2*pi*(0.125+detaf *n; xk1=fft(x,N;subplot(2,1,2;stem(n,abs(xk1;title('N=16,Δf=1/64';N=128;detaf=1/16;n=0:N-1;x=sin(2*pi*0.125*n+cos(2*pi*(0.125+detaf *n; xk=fft(x,N;figure(2;subplot(2,1,1;stem(n,abs(xk;title('N=128,Δf=1/16';detaf=1/64;x=sin(2*pi*0.125*n+cos(2*pi*(0.125+detaf *n; xk1=fft(x,N;subplot(2,1,2;stem(n,abs(xk1;title('N=128,Δf=1/64';2.5clcclose allN=16;p=8;q=2;a=.1;f=.0625;n=0:N-1;xa=exp(-(n-p.^2/q;xb=exp(-a*n.*sin(2*pi*f*n;xak=fft(xa,N;xbk=fft(xb,N;f=ifft(xak.*xbk,N;figure(1;subplot(4,1,1;stem(0:N-1,xa;title('xa(n=exp(-(n-p^2/q'; subplot(4,1,2;stem(0:N-1,xb;title('xb(n=exp(-a*n*sin(2*pi*f*n'; subplot(4,1,3; stem(0:N-1,f;title('xa(n⊙xb(n';xak1=fft(xa,2*N;xbk1=fft(xb,2*N;h=ifft(xak1.*xbk1,2*N;subplot(4,1,4;stem(0:2*N-2,h(1:2*N-1;title('xa*xb';2.6clcclose allN=512;xe=rand(1,N-0.5;for m=0:7;if(0<=m & m<=3xc(m+1=m;elseif(4<=m & m<=7xc(m+1=8-m;endendxck=fft(xc,71;f=0:518;fm=0:141;for m=1:8;xm=xe((m-1*64+1:m*64; xmk=fft(xm,71;fm(1:71=fm(72:142;fm(72:142=ifft(xmk.*xck,71; if m==2f(1:7=fm(1:7;endif m>1f((m-2*64+8:(m-1*64=fm(8:64;f((m-1*64+1:(m-1*64+7=fm(65:71+fm(72 :78; endif m==8f((m-1*64+8:m*64+7=fm(79:142;endendstem(0:512+6,f;%%%%重叠相加法title('重叠相加法';for m=1:8xm1(8:71=xe((m-1*64+1:m*64;if m==1xm1(1:7=0;else xm1(1:7=xe((m-1*64-6:(m-1*64;endxmk1=fft(xm1,71;fm1=ifft(xmk1.*xck,71;f1((m-1*64+1:m*64=fm1(8:71; endxmk2=fft(xe(506:512,71;h=ifft(xmk2.*xck,71;f1(513:519=h(8:14;figure(2stem(0:518,f1;title('重叠保留法';fa=conv(xc,xe;detaf=f1-f;figure(3;stem(0:518,detaf;2.7clcclose allN=16;p=8;q=2;a=.1;n=0:N-1;f=0.0625;xa=exp(-(n-p.^2/q;xb=exp(-a*n.*sin(2*pi*f*n; xak=fft(xa,N*2;xbk=fft(xb,2*N;rm=real(ifft(conj(xak.*xbk; rm=[rm(N+2:2*N rm(1:N]; m=(-N+1:N-1;stem(m,rm;title('线性相关';figure(2;xak1=fft(xa,N;xbk1=fft(xb,N;rm1=real(ifft(xak1.*xbk1,N; stem(n,rm1;3.1clearclose allwc=2*1000*tan(2*pi*300/(2*1000; wt=2*1000*tan(2*pi*200/(2*1000;[N,wn]=cheb1ord(wc,wt,0.8,20,'s'; [B,A]=cheby1(N,0.8,wn,'high','s';[num,den]=bilinear(B,A,1000; [h,w]=freqz(num,den;f=w/pi*500;plot(f,20*log10(abs(h;axis([0,500,-80,10];grid;xlabel('频率/Hz';ylabel('幅度/dB';3.2clear;close all;wc=2*pi*200;wr=2*pi*300;[n1,wn1] = buttord(wc,wr,1,25,'s'; [B,A]=butter(n1,wn1,'low','s';[num1,den1]=impinvar(B,A,1000; [h1,w]=freqz(num1,den1;wc=2*1000*tan(2*pi*200/(2*1000; wr=2*1000*tan(2*pi*300/(2*1000; [n,wn] = buttord(wc,wr,1,25,'s'; [B,A]=butter(n,wn,'low','s';[num2,den2]=bilinear(B,A,1000; [h2,w]=freqz(num2,den2;f=w/pi*500;plot(f,20*log10(abs(h1,'-.',f,20*log10(abs(h2 ,'-';legend('脉冲响应不变法','双线性变换法'; axis([0,500,-80,10] grid;xlabel('频率/Hz';ylabel('幅度/dB';3.3clearclose allwc=2*8000*tan(2*pi*1200/(2*8000;wr=2*8000*tan(2*pi*2000/(2*8000;[n,wn]=buttord(wc,wr,0.5,40,'s';[B,A]=butter(n,wn,'low','s';[num,den]=bilinear(B,A,8000;[h1,w]=freqz(num,den;[n,wn]=cheb1ord(wc,wr,0.5,40,'s';[B,A]=cheby1(n,0.5,wn,'low','s';[num,den]=bilinear(B,A,8000;[h2,w]=freqz(num,den;[n,wn]=ellipord(wc,wr,0.5,40,'s';[B,A]=ellip(n,0.5,40,wn,'low','s';[num,den]=bilinear(B,A,8000;[h3,w]=freqz(num,den;f=w/pi*4000;plot(f,20*log10(abs(h1,'-.',f,20*log10(abs(h2 ,'.-',f,20*log10(abs(h3,'-'; axis([0,4000,-100,10];grid;xlabel('频率/Hz';ylabel('幅度/dB';legend('Butterworth','Chebyshev','Ellicptic' hold onx=1200;plot(x3.4clearclose all;[n,wc]=buttord([2000 3000],[1500 6000],3,20,'s';[B,A]=butter(n,wc,'bandpass','s';[num,den]=bilinear(B,A,30000;[h1,w]=freqz(num,den;[num,den]=impinvar(B,A,30000;[h2,w]=freqz(num,den;f=w/pi*15000;plot(f,20*log10(abs(h1,'-.',f,20*log10(abs(ab s(h2;grid on;axis([0,3000,-100,0];legend('脉冲响应不变法','双线性变换'; xlabel('频率/Hz';ylabel('幅度/dB';3.5clearclose allw1=2*10000*tan(2*pi*1000/(2*10000;w2=2*10000*tan(2*pi*2000/(2*10000;w3=2*10000*tan(2*pi*500/(2*10000;w4=2*10000*tan(2*pi*3000/(2*10000; [n,wn]=cheb1ord([w3 w4],[w1 w2],3,18,'s' [B,A]=cheby1(n,3,wn,'stop','s';[num,den]=bilinear(B,A,10000;[h,w]=freqz(num,den;f=w/pi*5000;plot(f,20*log10(abs(h;axis([0,5000,-100,0];gridxlabel('频率/Hz';ylabel('幅度/dB';4.1%N=45,计算并画出矩形框、汉明窗、布莱克曼窗的归一化的幅度谱,并比较各自的主要特点%(1矩形窗(Rectangle Window调用格式:w=boxcar(n,根据长度n 产生一个矩形窗w。