Hilbert - Huang - guide

>> t(1)=1850; >> t(2)=2010; >> y1(1)=0; >> y1(2)=0; >> y2(1)=-0.3; >> y2(2)=-0.3; >> y3(1)=-0.6; >> y3(2)=-0.6; >> y4(1)=-0.9; >> y4(2)=-0.9; >> y5(1)=-1.2; >> y5(2)=-1.2; >> y6(1)=-1.6; >> y6(2)=-1.6; >> plot(t,y1,'k-'); >> hold on;

>> plot(t,y2,'k-'); >> plot(t,y3,'k-'); >> plot(t,y4,'k-'); >> plot(t,y5,'k-'); >> plot(t,y6,'k-'); >> plot(year,rslt(:,1)); >> plot(year,rslt(:,3)-0.3); >> plot(year,rslt(:,4)-0.6);

>> plot(year,rslt(:,5)-0.9); >> plot(year,rslt(:,6)-1.2);

>> plot(year,sum(rslt(:,7:8),2)-1.6,'r-'); >> set(gca,'yTickLabel',[]);

>> title('EEMD decomposition of GSTA (A_n=0.2; N_e_s_b=100)') >> axis([1850 2010 -2.1 0.2]); >> xlabel('year');

5) Statistical significance test

Since the annual mean global surface temperature anomaly behaves completely different from a white noise series, we use computer generated white noise to illustrate how the significance.m can be used:

>> clear; >> clf;

>> data=randn(512,1); >> rslt=eemd(data,0,1); >> imfs=rslt(:,2:8);

>> [sigline95,logep]=significance(imfs,0.05); >> [sigline99,logep]=significance(imfs,0.01); >> plot(sigline95(:,1),sigline95(:,2)); % 95 percenta line >> hold on

>> plot(sigline99(:,1),sigline99(:,2),'m-'); % 99 percenta line

>> plot(logep(:,1),logep(:,2),'r*'); >> plot(logep(1,1),logep(1,2),'k*'); >> grid;

>> xlabel('LOG2 ( Mean Period )');

>> ylabel('LOG2 ( Mean Normalized Energy )');

>> title('Significance test of IMFs of white noise'); >> axis([0 10 -7 0])

3) Trend and detrending

For example, in the previous decomposition, the sum of the last three columns satisfies the definition of trend well.

>> plot(year, rslt(:,1)); >> hold on;

>> plot(year, sum(rslt(:,7:8),2),'r-'); >> plot(year, sum(rslt(:,6:8),2),'g-'); >> plot(year, sum(rslt(:,5:8),2),'m-'); >> title('Trends of different timescales'); >> ylabel('Kelvin'); >> xlabel('year'); >> grid;