package_emd.rar_EMD 工具箱_imf_局部均值分解_模态分解包络_试验模态

/* * G. Rilling, last modification: 3.2007 * gabriel.rilling@ens-lyon.fr * * code based on a student project by T. Boustane and G. Quellec, 11.03.2004 * supervised by P. Chainais (ISIMA - LIMOS - Universite Blaise Pascal - Clermont II * email : pchainai@isima.fr). */ /************************************************************************/ /* */ /* INITIALIZATION OF EXTREMA STRUCTURE */ /* */ /************************************************************************/ extrema_t init_extr(int n) { extrema_t ex; ex.ind_min=(int *)malloc(n*sizeof(int)); ex.ind_max=(int *)malloc(n*sizeof(int)); ex.x_min=(double *)malloc(n*sizeof(double)); ex.x_max=(double *)malloc(n*sizeof(double)); ex.ry_min=(double *)malloc(n*sizeof(double)); ex.ry_max=(double *)malloc(n*sizeof(double)); ex.iy_min=(double *)malloc(n*sizeof(double)); ex.iy_max=(double *)malloc(n*sizeof(double)); return ex; } /************************************************************************/ /* */ /* DETECTION OF LOCAL EXTREMA */ /* */ /************************************************************************/ void extr(double x[], COMPLEX_T z[], double phi,int n,extrema_t *ex) { int cour; double val,valp,valn; #ifdef C99_OK COMPLEX_T eiphi; #endif ex->n_min=0; ex->n_max=0; #ifdef C99_OK eiphi = cexp(I*phi); #endif #ifdef C99_OK val = CREAL(eiphi*z[0]); #else val = crealeiphi(phi,z[0]); #endif #ifdef C99_OK valn = CREAL(eiphi*z[1]); #else valn = crealeiphi(phi,z[1]); #endif /* search for extrema in direction phi*/ for(cour=1;cour<(n-1);cour++) { valp = val; val = valn; #ifdef C99_OK valn = CREAL(eiphi*z[cour+1]); #else valn = crealeiphi(phi,z[cour+1]); #endif if (val<valp && val<valn) /* local minimum */ { ex->x_min[ex->n_min+NBSYM]=x[cour]; ex->ry_min[ex->n_min+NBSYM]=CREAL(z[cour]); ex->iy_min[ex->n_min+NBSYM]=CIMAG(z[cour]); ex->ind_min[ex->n_min+NBSYM]=cour; ex->n_min++; } if (val>valp && val>valn) /* local maximum */ { ex->x_max[ex->n_max+NBSYM]=x[cour]; ex->ry_max[ex->n_max+NBSYM]=CREAL(z[cour]); ex->iy_max[ex->n_max+NBSYM]=CIMAG(z[cour]); ex->ind_max[ex->n_max+NBSYM]=cour; ex->n_max++; } } } /************************************************************************/ /* */ /* EXTRAPOLATION OF EXTREMA TO LIMIT BORDER EFFECTS */ /* */ /************************************************************************/ void boundary_conditions(double x[],COMPLEX_T z[],double phi,int n,extrema_t *ex) { int cour,nbsym; #ifdef C99_OK COMPLEX_T eiphi; #endif #ifdef C99_OK eiphi = cexp(I*phi); #endif nbsym = NBSYM; /* reduce the number of symmetrized points if there is not enough extrema */ while(ex->n_min < nbsym+1 && ex->n_max < nbsym+1) nbsym--; if (nbsym < NBSYM) { for(cour=0;cour<ex->n_max;cour++) { ex->ind_max[nbsym+cour] = ex->ind_max[NBSYM+cour]; ex->x_max[nbsym+cour] = ex->x_max[NBSYM+cour]; ex->ry_max[nbsym+cour] = ex->ry_max[NBSYM+cour]; ex->iy_max[nbsym+cour] = ex->iy_max[NBSYM+cour]; } for(cour=0;cour<ex->n_min;cour++) { ex->ind_min[nbsym+cour] = ex->ind_min[NBSYM+cour]; ex->x_min[nbsym+cour] = ex->x_min[NBSYM+cour]; ex->ry_min[nbsym+cour] = ex->ry_min[NBSYM+cour]; ex->iy_min[nbsym+cour] = ex->iy_min[NBSYM+cour]; } } /* select the symmetrized points and the axis of symmetry at the beginning of the signal*/ if (ex->x_max[nbsym] < ex->x_min[nbsym]) { /* first = max */ #ifdef C99_OK if (CREAL(eiphi*z[0]) > CREAL(eiphi*z[ex->ind_min[nbsym]])) { /* the edge is not a min */ #else if (crealeiphi(phi,z[0]) > crealeiphi(phi,z[ex->ind_min[nbsym]])) { /* the edge is not a min */ #endif if (2*ex->x_max[nbsym]-ex->x_min[2*nbsym-1] > x[0]) { /* symmetrized parts are too short */ for(cour=0;cour<nbsym;cour++) { ex->x_max[cour] = 2*x[0]-ex->x_max[2*nbsym-1-cour]; ex->ry_max[cour] = ex->ry_max[2*nbsym-1-cour]; ex->iy_max[cour] = ex->iy_max[2*nbsym-1-cour]; ex->x_min[cour] = 2*x[0]-ex->x_min[2*nbsym-1-cour]; ex->ry_min[cour] = ex->ry_min[2*nbsym-1-cour]; ex->iy_min[cour] = ex->iy_min[2*nbsym-1-cour]; } } else { /* symmetrized parts are long enough */ for(cour=0;cour<nbsym;cour++) { ex->x_max[cour] = 2*ex->x_max[nbsym]-ex->x_max[2*nbsym-cour]; ex->ry_max[cour] = ex->ry_max[2*nbsym-cour]; ex->iy_max[cour] = ex->iy_max[2*nbsym-cour]; ex->x_min[cour] = 2*ex->x_max[nbsym]-ex->x_min[2*nbsym-1-cour]; ex->ry_min[cour] = ex->ry_min[2*nbsym-1-cour]; ex->iy_min[cour] = ex->iy_min[2*nbsym-1-cour]; } } } else { /* edge is a min -> sym with respect to the edge*/ for(cour=0;cour<nbsym;cour++) { ex->x_max[cour] = 2*x[0]-ex->x_max[2*nbsym-1-cour]; ex->ry_max[cour] = ex->ry_max[2*nbsym-1-cour]; ex->iy_max[cour] = ex->iy_max[2*nbsym-1-cour]; } for(cour=0;cour<nbsym-1;cour++) { ex->x_min[cour] = 2*x[0]-ex->x_min[2*nbsym-2-cour]; ex->ry_min[cour] = ex->ry_min[2*nbsym-2-cour]; ex->iy_min[cour] = ex->iy_min[2*nbsym-2-cour]; } ex->x_min[nbsym-1] = x[0]; ex->ry_min[nbsym-1] = CREAL(z[0]); ex->iy_min[nbsym-1] = CIMAG(z[0]); } } else { /* first = min */ #ifdef C99_OK if (CREAL(eiphi*z[0]) < CREAL(eiphi*z[ex->ind_max[nbsym]])) { /* the edge is not a max */ #else if (crealeiphi(phi,z[0]) < crealeiphi(phi,z[ex->ind_max[nbsym]])) { /* the edge is not a max */ #endif if (2*ex->x_min[nbsym]-ex->x_max[2*nbsym-1] > x[0]) { /* symmetrized parts are too short */ for(cour=0;cour<nbsym;cour++) { ex->x_max[cour] = 2*x[0]-ex->x_max[2*nbsym-1-cour]; ex->ry_max[cour] = ex->ry_max[2*nbsym-1-cour]; ex->iy_max[cour] = ex->iy_max[2*nbsym-1-cour]; ex->x_min[cour] = 2*x[0]-ex->x_min[2*nbsym-1-cour]; ex->ry_min[cour] = ex->ry_min[2*nbsym-1-cour]; ex->iy_min[cour] = ex->iy_min[2*nbsym-1-cour]; } } else { /* symmetrized parts are long enough */ for(cour=0;cour<nbsym;cour++) { ex->x_max[cour] = 2*ex->x_min[nbsym]-ex->x_max[2*nbsym-1-cour]; ex->ry_max[cour] = ex->ry_max[2*nbsym-1-cour]; ex->iy_max[cour] = ex->iy_max[2*nbsym-1-cour]; ex->x_min[cour] = 2*ex->x_min[nbsym]-ex->x_min[2*nbsym-cour]; ex->ry_min[cour] = ex->ry_min[2*nbsym-cour]; ex->i