Working Examples

Here, the use of our programs is demonstrated:

Firstly, we create three ideals signals, namely y, x1 and x2. y comprises of sine waves of period


t=[-100:1:100];
y=sin(t*2*pi)+sin(t*2*pi/4)+sin(t*2*pi/8)+sin(t*2*pi/16)+sin(t*2*pi/32)+sin(t*2*pi/64);
x1=sin(t*2*pi/4);
x2=sin(t*2*pi/16);

The corresponding wavelet power spectrum can be plotted using Aslak Grinsted's Matlab function inside the combined software package (you should have this function ready when combining our software package with that of Aslak Grinsted, see Download page):

fig1
subplot(3,1,1);
wt(y);

subplot(3,1,2);
wt(x1);

subplot(3,13);
wt(x2);
Partial wavelet coherence

The partial wavelet conherence squared on y and x1 to reveal their stand-alone relationship (after the removal of the influence of x2):

fig2
pwc(y, x1, x2);
Multiple wavelet coherence

The multiple wavelet coherence squared of y, x2 and x1, which gives the resulting wavelet coherence squred that computes the proportional of wavelet power of the y explained by x2 and x1:

fig3
mwc(y, x2, x1);
Rectified wavelet power specturm

The bias problem of wavelet power spectrum found in previous software packages (top) is rectified (bottom) according to Liu et al. (2007):

pic4
subplot(2,1,1);
wt(y);

subplot(2,1,2);
wtrec(y);
Rectified wavelet cross specturm

The bias problem of wavelet power spectrum found in previous software packages (top) is rectified (bottom) according to Veleda et al. (2012):

fig5
subplot(2,1,1);
xwt(y,y);

subplot(2,1,2);
xwtrec(y,y);

Should you have any enquiry, please feel free to contact:
Eric K. W. Ng
Email: E.Ng@my.cityu.edu.hk