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发表于 2011-3-29 13:24:52
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回复 2# debra [, \5 V) P* C3 V
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7 X0 H* z- v8 S) \, C8 H %打开指定文件,并对信号进行Pon分析计算
4 e/ k* ?# Q3 `) zfunction [M, Amp, Fre, damp, Pha, main_f, main_damp, x, xc, y, Amp_Response, er, all, N, dt]=x_svdprony(x_in, dt, fL, showfigure)" T5 M. r8 X W/ M# @
format long;/ D+ q: n4 ~: _& a. W+ z: P
x = x_in';* P9 D4 q% F$ X5 p3 q
cpu=cputime;: l) E' r2 K( }1 M F9 ? W' ~, ?1 \9 t
N=size(x,1);
7 }0 x8 ?2 `) c, m %取N/2的整数部分为初始的P
9 Z* p+ p1 z# M5 |2 ~, I, t- @ P=floor(N/2);
/ ?* q3 ]5 V7 @% b6 e % \' @1 U) J& q/ O- V4 l
%去直流环节
* @/ `5 | ^* u+ f+ p4 i x_Sum = 0;
- J: `1 _" v8 c1 Z( r for i=1:N" X% Q' \5 o+ Z
x_Sum = x_Sum + x(i);/ W! j. O5 Z1 ]2 T. z6 q
end
3 k. Z: O# P: s# w; B: I x_av = x_Sum / N;
^8 W2 Z9 u8 {0 U. ^' s if x_av > 10E-10% D: j# {* X, [9 w) Z3 Q Q; d
for i=1:N: I6 E: Z3 K* q4 p9 G" ]
x(i) = x(i) - x_av;! P1 \! Y; Z0 @( ]6 B
end
+ L# w4 ]) y- z4 P end; p* f b& r4 Q, a
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2 U8 j/ J3 v# o4 h) [ e %滤波环节# l3 ?9 Y+ j# ~) ^! ^9 ~ d
%fL=1;0 O' p6 Y2 F& B/ {9 L4 y
if fL>1/ I% Y' M! N- U
for i=fL+1:N: y* z7 X0 o- J% _* `
x(i-fL)=0;; t$ m5 _7 o3 T# O3 k5 n
for j=1:fL
" u& b: ]: r. B9 P, W# N+ f3 s x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);# ^' i ~' D: B
end
: R& w% t% `- N7 x; I# I# f end
: b o& B9 q( D1 G z |" a end
8 J3 Q# Y- l, e. [1 p/ ]; J N=N-fL;
) e0 L( [. j9 p& T d4 \! S tt=0:1:N-1;
) b9 ?2 g( K5 w3 d/ W. @8 J/ R% A 5 h, f- d) \3 D; H C! K4 M
%P要求为偶数
5 R# u; ^. `1 n j. W( e1 C, d. G5 D) @ if mod(P, 2) ~= 0% _) P0 d B |6 q
P = P - 1;8 e q+ _0 Q6 c/ f" h
end' `1 r$ Z$ Y, @# ^; x; h
5 {) e0 ]5 n5 H
P1=P;- c; B& n" S+ Y7 s. X/ Y+ u
if mod(P, 2) == 0& M2 e" T1 V% q ~( a, N g g& k
% Generate R,生成样本矩阵1 j. E, _5 Q, a: v6 |
for i=1:P1
8 Q" ~5 g \& S7 Q( f: J for j=1:P1+1 }' y; W5 [5 O& L( u7 x) w
ss=0;
5 W' q0 y) [; Q$ C: E3 m for k=P1:N-1
0 x/ C$ L0 |, e" h$ U %前向预测误差1 }( ^; r9 z3 v
ss=ss+x(k+2-j,1)*x(k+1-i,1);
5 ^& ?6 y( ?4 Q7 [+ B+ _6 u %后向预测误差
+ y2 X( L' J* y Q %ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
, ?& Y; k: t6 x %同时考虑双向误差
; o' f0 ^% `4 L7 p9 g9 o %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
: P3 _8 S3 ~4 Z) ?0 b3 S end + S" g# W J1 L8 d' R7 v
R(i,j)=ss;
0 L, d0 Q% a1 r: P4 T& `' _ end! ~7 `& E4 M( @
end
7 } u. m- a+ a % divide R into R1 and R2, and get A; R1*A=R2;
1 ?2 M! b1 ~ L! v V0 ]& m% i8 p* q for i=1:P
7 q& C( X* o3 `2 [( b for j=1:P* N6 l, V9 M9 N# D) l: @" O1 f
R1(i,j)=R(i,j+1);
! _5 e$ r1 P: G, U$ `$ [ end
& N4 M, W2 D: Y; d: J3 A$ x/ { end
( `2 R0 s$ H& X1 a for i=1:P
# Y0 j+ {$ \2 Q& |' g" T5 n+ _ R2(i)=R(i,1);
. U6 z& A- m) i3 g f end
, |- t2 I2 z- B( K9 A, F
* l) q' y# e: r$ B %添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%9 R' ?8 o a6 f3 M
%首先进行SVD分解
( u1 w2 ~4 W3 @9 M+ s [u,s,v]=svd(R1);
; |. h% \/ w. H, ?! W %根据奇异值确定实际的阶数M
; u9 T) a% b+ _; Z: _5 G. {5 \7 Q! {/ o M=0;9 k. I* _! @ C& h* e8 O
%计算全部奇异值的均方和! Z8 G1 g( G; m$ S+ @$ q
Sum_SVD=0;
% g. @1 J: z# g* O for i=1:P' T: B6 @- i1 D9 M
Sum_SVD = Sum_SVD+s(i,i)^2;6 W( H* Y4 T/ Z2 f2 s& l/ b
end6 {/ x7 Q9 A& u6 q; t) n& q- G
cur_sum = 0;
% }( p' c3 t B- o7 |% { i=1;9 U( F% G. I* v8 b" N2 L
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P
0 V" ]( E' N: V. P" x% j6 ~ cur_sum = cur_sum + s(i,i)^2;3 M0 z$ m/ y" k e( J$ {
M = M + 1;
( L2 d! z9 b6 Q+ F) p1 h i = i + 1;
; ^' E& _* t; d | end+ d7 j$ i' Z9 Q
%输出预测的阶数M
4 k% w9 F5 K L M;# Z1 v/ M' m7 [
%生成Sp矩阵) V) t7 Q" l( P9 m9 o
Sp=zeros(M+1, M+1);8 V' N9 w4 _& \; x& l
for j=1:M
}7 Z! t& u; T for i=1:(P-1)-M+1( G3 s# n" V$ u- A2 e
Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';
( `# v0 R1 _* U1 M" d7 p end
5 Q8 S& o" b, R6 O7 W( O/ ` end
# K/ A5 }9 i8 l# i 5 b# p, @! e5 n' C: q' H c
%根据公式生成最佳最小二乘解
6 T6 u7 M* D: K$ A( a7 ~ Sp_inv=inv(Sp);
. b' X4 H1 Y8 N. d) E5 c. K, d H+ { if isinf(Sp_inv(1,1)) == 11 u* c( [) |5 V$ L/ K9 h: i2 ~- }
Sp_inv = pinv(Sp);% i& c: p8 B) g4 c o. L9 y) X Z
end
" p7 D) H: Z! l0 n5 F0 y7 _ . v! [% r8 }1 L+ p% s
a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
; \0 v- L( }9 }# I5 M P = M;
6 T% G* J o& C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 P! X- l' @& y+ y1 a6 _ % Get Zi
5 D! @* z4 i0 r1 Z& H cof_SVD(1)=1; ?7 u. N( \+ g0 @) s" U7 u' A
for i=1:M# E$ o1 t1 J% D; T: M+ _
cof_SVD(i+1)=a_SVD(i);
+ ~/ I) f8 c+ `7 u) K' [ end
, J. l2 ^& C, M Z=roots(cof_SVD);
# \! u7 g1 l4 Z+ a' @ b5 s3 t
, M& a! Y9 k! N3 v3 H % Get y,y should be very close to x- w3 B* ^) J3 f0 X; n7 K) a
for i=1:P
1 A- m! ~, o% A+ F* h( k& ? y(i)=x(i);3 A* }8 \* A# o+ R- a# q8 ^; j1 u
end4 X9 \; c% u& d& q
6 G- N8 t9 k6 u" n9 [. X
for i=P+1:N
3 c9 |: \9 I) P8 Z( S9 G. R# u1 S$ b y(i)=0;+ J0 Q- ?$ Q, \
end
% E* @9 | N# V' d- a for i=P+1:N9 d% d) R. [# z" |/ A, {: _8 P
for j=1:P
; s9 o2 V! g7 m& d y(i)=y(i)-a_SVD(j)*x(i-j);% e. U: p8 {! [) {
end( ]" ]( y; J# V! k/ n! f( Y
end$ Q/ d2 @1 v+ b; g1 c$ d
& k: A! r, H0 L* B! M0 V% R % Get B
9 a/ p2 X$ x" _5 X0 j* ]! f for i=1:N4 l; ^. R; Y* n; B7 f
for j=1:P
. P1 M5 u1 e$ z6 G; n9 t Fy(i,j)=Z(j)^(i-1);
+ a0 |( c# S, z8 _# c$ h end
" h$ o( l, O. y# f( L! a: y3 [2 U end
# f( t9 p, _7 p' D( E4 w1 U Y. D Fz=Fy';2 \4 _% M. E9 v7 D0 {; Z: A% D
FH=Fy'*Fy;' a1 s* K5 h0 v; z) g
Fn=inv(FH);
2 s& s! ~7 h. n! |0 C- p* \) { B = inv(Fy'*Fy)*Fy'*y';
" w8 g/ W( _' v" ^: y- q , z' ^6 z i8 I/ D5 I# \0 S" ^+ J, L
% Calculate Amplitude, Phasor, Frequency and damp. Z* O, ~; J1 a9 n6 s4 D2 s6 u( d6 J
for i=1:P6 i) z0 G# b3 t: P' S1 ~
Amp(i)=abs(B(i));
Y- l7 v# \3 q: \ Pha(i)=atan(imag(B(i))/real(B(i)));
8 i: k7 W p' R! {; t Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);
# n4 B M# W7 j damp(i)=log(abs(Z(i)))/dt;. S2 O3 v# i8 T7 D6 l! n
end
+ F6 @$ o9 f" [6 A. l- { %调试用的代码) G: f+ ^. r7 O5 K
if isnan(Amp(1)) == 19 [5 N. z! [8 q g: D( `' K; u
error('幅值的求解出现错误!');* D! y# l* b* o; F; Q3 u; @
end
5 z" T' g3 r& z
" |0 V, @* \9 p* K % Get xc,verify if xc is nearly equal to x
3 M- |0 |* \9 m4 O# [ l for i=1:P2 Q2 v/ ?/ w- M) f
if(real(B(i))>=0.0)! p3 H- S* b/ x* U! L. u
bth(i)=Pha(i);
1 n' q- B$ F2 X$ m* m else. t* i; U& X$ {
bth(i)=pi+Pha(i);# |- Z$ e* x, X6 u6 ~
end; h; Y! {9 c9 T; r0 N. [2 X) ~
end
1 C# z+ g; g, R) O# a %对Pha重新幅值
: P+ d3 j2 }- C2 u1 J/ [5 O for i=1:P
5 r/ a/ K8 a( E* O$ [& R% [ if Pha(i) < 0: j, L; n/ d5 e4 g5 a. z& Z; I
Pha(i) = Pha(i) + 2*pi;! Q. q* a0 i. k% O- W* n8 \
end+ t6 V5 _. P; A- r
end
. ^* L% Z, x2 f2 N7 G B) ^ 7 `4 w+ d$ ?7 k, q' x! C
for i=1:N
! `; F" m, y% ]0 @- W4 L xc(i)=0.0;
+ X# H a7 t' Q# a- Q* q% v. X) X. ~ for j=1:P
5 l; F: b( ?4 V' N xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));
) b% Q) `! ^1 _ end
, k) d4 q; l3 f end6 Y* o; G; F8 E }2 C$ I7 j
% if showfigure == 1
2 P7 z" }" s8 j- g# l% %显示特征根的位置7 D! l- X; }3 m- M3 J" g1 d4 u
% figure;
$ a7 `; r/ W+ n7 z! D6 G# }% plot(damp, 2*pi*Fre, 'r*');8 V" k' e( `- t5 p# r
% end1 h' s6 M- ^/ \
/ f& Z1 H2 u. L# ^3 K0 d, y xj=xc';
9 P+ d$ M' p% ~6 b9 ^" S( z" v er=0;) J" C# k, \: x# H+ ^" V
all = 0;
6 B, j* Z: _4 X& D for i=1:N 7 Z( P5 ~ S- @
er=er+(x(i)-xc(i))^2;
- r8 v5 ~, V! Z! R5 O1 o all = all+x(i)^2;
0 t# }5 U' }$ L' u end9 e8 L1 P3 n/ N( H3 y3 t
SNR=-20*log(sqrt(er/all));
* C4 W8 L! C! {/ c( B# W: A |" B# C# F8 P& U( H
% Calculate Prony spectrum% N7 E2 G5 f6 T& w' n8 N9 d
%频谱的取值范围为0-5Hz
4 I; b2 \$ k6 A i f=0:0.01:4.99;
4 s' Y4 m4 C% p9 H for j=1:size(f,2)4 v( c5 L" k& L+ H
sptr(j)=0;
. O5 h- ]! }( C2 ~* H sptr1(j)=0;/ Y: a0 Z$ `% p6 ~ ^$ k5 b
sptr2(j)=0;0 j/ z0 ?9 N1 R' Q( e. `
angl(j)=0;
, j3 R. n. l2 t+ @1 h# s tmpangle = 0;
W1 s K4 ]# | for k=1:P* ~$ I. S$ K1 n' T7 k
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
9 c9 {) V( D# H) f } sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
7 y e ?0 c3 E8 F1 Y1 o1 V end# H9 g; ?% R7 I# S+ M/ u6 M/ l5 M
sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);, s8 v8 _+ W1 j
tmpangle = atan2(sptr1(j),sptr2(j));( g# [+ Z" E# i9 z# }
angl(j) = tmpangle*360/pi;: ~. m/ R) @8 {/ X) ?) ?& N$ `" z
end3 ]$ u( u- }( b1 i
%对幅频响应进行归一化,并且寻找主导频率模式# I) `# \0 s7 P3 q: Z
%寻找sptr的最大值4 e. ?7 G" r O1 Y+ b, L; a
max_sptr=0;6 ?& ?9 t) T% k, n2 L
main_f=0;
* `. P0 [7 x% j. r0 b9 F& ? for j=1:size(f,2)
: r3 \7 y5 q) M! X$ t% s/ x if sptr(j) > max_sptr( O4 A3 u: _6 J4 `- q2 x
max_sptr = sptr(j);, z7 x G( l- _$ Y) ]; i9 |! v6 R
%主导频率出现在最大幅频响应位置
9 G; A! X! a1 c7 L, _ if f(j) ~= 0;# t) @- G6 {" L
main_f = f(j);# ^! x# B3 g/ d- J$ T4 w. e3 R% y# p& F
else. R, q( l& ~$ H) b
max_sptr = 0;
( X* f- R& H! K$ ?7 G end3 Q- V5 A9 F3 D1 ~0 }) @
end' h# z6 E( F5 g
end* b7 r5 o& n: y, ^- N
main_f;& Y1 v5 L3 @+ q/ _) p) G
%找出真正计算的频率值# a, y7 W1 m; D. e- @. W& }
f_err = 10;
6 ?% ?! G9 y& ~0 {! P7 r f_main = 0;
3 F+ w7 {( x8 C7 L for i=1:size(Amp, 2)
2 ~0 U5 o1 M/ M! ]* w5 N if abs(main_f - Fre(i)) < f_err* L5 a/ P4 b3 P7 B$ h
f_main = Fre(i);* p8 T/ c% G0 X' ], E7 }
damp_main = damp(i);
; y5 F+ h: K8 r8 B5 f5 u8 {/ L f_err = abs(main_f - Fre(i));
a9 j1 _2 Q0 L! m end
% e* ]8 y: [ _$ }& B6 n end
! H9 h8 ~2 D1 h5 h main_f = f_main;9 h' ~: ^% t: [6 P: n9 z! v
main_damp = damp_main;. t u# E" h! {3 a
%进行归一化1 Y# A5 ]/ s; X5 `+ f& r
for j=1:size(f,2)( `4 o; X$ `- @$ C/ Q1 V4 U
sptr(j)=sptr(j)/max_sptr;% t3 R$ W v a- J& d
Amp_Response(j) = sptr(j);* K% D8 Y4 U: ?, S3 R! W M$ i
end- I. ?0 W( S: U' I
: H" v6 t; i$ K6 F0 B3 s for i=1:size(f,2). [: S2 L' \, Q4 n. z
if angl(i) > 0
- b% l- }! B; }7 |+ Q; i9 e# `5 H1 k$ ~3 _ angl(i)=angl(i)-360;, d& R$ N9 W, A/ u1 r
end
* y4 ?- f; ]9 G2 E end
7 l1 a3 V3 Y) B& R# r 7 I$ i# b7 n2 e: T, `' |
if showfigure == 1
: v/ J# B6 |! d- P& A4 W% R %在一个图上显示时域拟和曲线和Prony频谱分布
; R& I9 H3 s& b( m figure;6 V) v" z6 l3 J. Q# h9 \0 }8 ~! q
subplot(2,1,1);) V! D" k7 \4 @; _0 I+ o1 i
%plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');' O1 D* J7 v% i' g0 x
plot(tt,x(1:N),'r', tt,xc, '*b');
: U- I' k9 B' ]! B! g, R6 r( S/ H subplot(2,1,2);" \6 c4 U1 m" N4 L5 A. y) s
plot(f,sptr);8 {) \' ^1 P7 e" K4 o7 U: t
%subplot(2,2,3);
8 ?$ s* W8 Q7 R9 n6 m% o %plot(f,sptr);& V6 ]: ^6 V# n* A7 \+ T
%subplot(2,2,4);( P0 @% f% E/ w8 N+ B, B
%plot(f,angl);
9 \9 @" I, v3 G# P u' b. k8 A end' ^+ U) ^. @: e+ n( |* z2 J" `! Q
% C/ |& p1 c6 [' X cpu=cputime-cpu;
/ I F5 \/ Z8 s format short;1 [. e! i1 _; |, z) v. n
end |
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