# Differences observed on the complex wavelet transform applied on the same signal

I have applied a complex wavelet transform on two signals :

1. a first one
2. 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 !

@Jazzmaniac

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).

• You should provide more details how exactly those two graphs are generated. – Jazzmaniac Dec 9 '13 at 21:12
• I don't know python code, have you used CWT? what wavelet function have you used? what does this line means? y1 = numpy.abs(dtcwt.dtwavexfm(x1,8)) thanks. @xavier-r – Electricman Dec 10 '13 at 19:33
• I have used a complex wavelet transform. This line is performing the decomposition, and then calculating the module. You can see the documentation of the function here : dtwavexfm doc – Xavier R. Dec 11 '13 at 9:37