derive1.m

信号分析与处理的一些源代码

syms a0 a1 b1 a2 b2 a3 b3 a4 b4 a5 b5 H1 H2 x;  %取n=5求解析解用matlab推导A0,Ai,Bi(i=1,...,7)
y=a0+a1*cos(x)+b1*sin(x)+a2*cos(2*x)+b2*sin(2*x)+a3*cos(3*x)...
+b3*sin(3*x)+a4*cos(4*x)+b4*sin(4*x)+a5*cos(5*x)+b5*sin(5*x);
dy=diff(y);
d2y=diff(dy);
z=d2y+2*(a+b*sin(2*x))*dy+(g+2*d*cos(2*x))*y-H1*cos(x)-H2*sin(x);
A0=simple((int(z,x,0,2*pi))/(2*pi));
A1=simple((int(z*cos(x),x,0,2*pi))/(pi));
B1=simple((int(z*sin(x),x,0,2*pi))/(pi));
A2=simple((int(z*cos(2*x),x,0,2*pi))/(pi));
B2=simple((int(z*sin(2*x),x,0,2*pi))/(pi));
A3=simple((int(z*cos(3*x),x,0,2*pi))/(pi));
B3=simple((int(z*sin(3*x),x,0,2*pi))/(pi));
A4=simple((int(z*cos(4*x),x,0,2*pi))/(pi));
B4=simple((int(z*sin(4*x),x,0,2*pi))/(pi));
A5=simple((int(z*cos(5*x),x,0,2*pi))/(pi));
B5=simple((int(z*sin(5*x),x,0,2*pi))/(pi));
A6=simple((int(z*cos(6*x),x,0,2*pi))/(pi));
B6=simple((int(z*sin(6*x),x,0,2*pi))/(pi));
A7=simple((int(z*cos(7*x),x,0,2*pi))/(pi));
B7=simple((int(z*sin(7*x),x,0,2*pi))/(pi));


syms a0 a1 b1 a2 b2 a3 b3 a4 b4 a5 b5 a b g d H1 H2 x;  %取n=5求解析解用matlab推导A0,Ai,Bi(i=1,...,7)
pA0a0=diff(A0,'a0');
pA0a2=diff(A0,'a2');
pA2a0=diff(A2,'a0');
pA1a1=diff(A1,'a1');
pA1b1=diff(A1,'b1');
pA1a3=diff(A1,'a3');
pB1a1=diff(B1,'a1');
pB1b1=diff(B1,'b1');
pB1b3=diff(B1,'b3');
pA2a2=diff(A2,'a2');
pA2b2=diff(A2,'b2');
pA2a4=diff(A2,'a4');
pB2a2=diff(B2,'a2');
pB2b2=diff(B2,'b2');
pB2b4=diff(B2,'b4');
pA3a1=diff(A3,'a1');
pA3a3=diff(A3,'a3');
pA3b3=diff(A3,'b3');
pA3a5=diff(A3,'a5');
pB3b1=diff(B3,'b1');
pB3a3=diff(B3,'a3');
pB3b3=diff(B3,'b3');
pB3b5=diff(B3,'b5');
pA4a2=diff(A4,'a2');
pA4a4=diff(A4,'a4');
pA4b4=diff(A4,'b4');
pB4b2=diff(B4,'b2');
pB4a4=diff(B4,'a4');
pB4b4=diff(B4,'b4');
pA5a3=diff(A5,'a3');
pA5a5=diff(A5,'a5');
pA5b5=diff(A5,'b5');
pB5b3=diff(B5,'b3');
pB5a5=diff(B5,'a5');
pB5b5=diff(B5,'b5');
pA6a4=diff(A6,'a4');
pB6b4=diff(B6,'b4');
pA7a5=diff(A7,'a5');
pB7b5=diff(B7,'b5');

AA=2*A0*pA0a0+A2*pA2a0;
BB=A1*pA1a1+B1*pB1a1+A3*pA3a1;
CC=A1*pA1b1+B1*pB1b1+B3*pB3b1;
DD=2*A0*pA0a2+A2*pA2a2+B2*pB2a2+A4*pA4a2;
EE=A2*pA2b2+B2*pB2b2+B4*pB4b2;
FF=A1*pA1a3+A3*pA3a3+B3*pB3a3+A5*pA5a3;
GG=B1*pB1b3+A3*pA3b3+B3*pB3b3+B5*pB5b3;
HH=A2*pA2a4+A4*pA4a4+B4*pB4a4+A6*pA6a4;
II=B2*pB2b4+A4*pA4b4+B4*pB4b4+B6*pB6b4;
JJ=A3*pA3a5+A5*pA5a5+B5*pB5a5+A7*pA7a5;
KK=B3*pB3b5+A5*pA5b5+B5*pB5b5+B7*pB7b5;

f1=BB;
f2=CC;
f3=FF;
f4=GG;
f5=JJ;
f6=KK;

m11=diff(f1,'a1');
m12=diff(f1,'b1');
m13=diff(f1,'a3');
m14=diff(f1,'b3');
m15=diff(f1,'a5');
m16=diff(f1,'b5');
m21=diff(f2,'a1');
m22=diff(f2,'b1');
m23=diff(f2,'a3');
m24=diff(f2,'b3');
m25=diff(f2,'a5');
m26=diff(f2,'b5');
m31=diff(f3,'a1');
m32=diff(f3,'b1');
m33=diff(f3,'a3');
m34=diff(f3,'b3');
m35=diff(f3,'a5');
m36=diff(f3,'b5');
m41=diff(f4,'a1');
m42=diff(f4,'b1');
m43=diff(f4,'a3');
m44=diff(f4,'b3');
m45=diff(f4,'a5');
m46=diff(f4,'b5');
m51=diff(f5,'a1');
m52=diff(f5,'b1');
m53=diff(f5,'a3');
m54=diff(f5,'b3');
m55=diff(f5,'a5');
m56=diff(f5,'b5');
m61=diff(f6,'a1');
m62=diff(f6,'b1');
m63=diff(f6,'a3');
m64=diff(f6,'b3');
m65=diff(f6,'a5');
m66=diff(f6,'b5');

a=0.3;b=0.01;g=1.14;d=0.11;

M=[m11 m12 m13 m14 m15 m16;m21 m22 m23 m24 m25 m26;m31 m32 m33 m34 m35 m36;...
   m41 m42 m43 m44 m45 m46;m51 m52 m53 m54 m55 m56;m61 m62 m63 m64 m65 m66]   

h1=-H1*diff(f1,'H1')-H2*diff(f1,'H2');
h2=-H1*diff(f2,'H1')-H2*diff(f2,'H2');
h3=-H1*diff(f3,'H1')-H2*diff(f3,'H2');
h4=-H1*diff(f4,'H1')-H2*diff(f4,'H2');
h5=-H1*diff(f5,'H1')-H2*diff(f5,'H2');
h6=-H1*diff(f6,'H1')-H2*diff(f6,'H2');

h=[h1;h2;h3;h4;h5;h6]