I have applied a complex wavelet transform on two signals :
- a first one
- a second one that is a concatenation of the first signal and another one
For the 4th coefficient (as an example, i've got the same problem for all of them), i get the following graph for its module (1- is blue, 2- is green) :
What could explain the differences observed between the two signals ? Seems like the coefficients don't have the same spectral width ?
Thank you !
The two graphs are (almost) generated as follow in python (i've generalized to sinus signals, and plotted every coefficients). In reality, not all the coefficients are different : only those in relation with signal frequencies.
import numpy import pylab import dtcwt f1 = 10. f2 = 15 w1 = numpy.pi * f1 w2 = numpy.pi * f2 time_interval = 100 samples = 50000 t = numpy.linspace(0, time_interval, samples) x1 = numpy.sin(w1 * t) x2 = numpy.sin(w2 * t)*1.5 x12 = numpy.array(list(x1)+list(x2)) y1 = numpy.abs(dtcwt.dtwavexfm(x1,8)) y2 = numpy.abs(dtcwt.dtwavexfm(x12,8)) for i in range(8): pylab.figure() pylab.plot(y1[i][50:150], '-x') pylab.plot(y2[i][50:150], '-x') pylab.grid() pylab.title('yh'+str(i)) pylab.legend(('Coil alone','2 coils')) pylab.show()
When i change x1 in :
x1 = numpy.array(list(x1)+list(x1))
I get exactly the same coefficients (ie. when x1 and x2 have the same length and x1 is "substantial" : filling the difference with zeros doesn't work).