CODEWITHSUNDEEP
pythonpython-2.7wavelet
user1283244
user1283244

Reputation: 21

Spectrum of Wavelet

I have a morlet wavelet which is described by a plane wave multiplied with a gaussian window, and a scaling parameter, s. I.e. in python language:

import numpy
f = 10
omega = 2*numpy.pi*f
x = numpy.linspace(-5,5,num=1000)
wavelet = numpy.exp(numpy.complex(0,1)*omega*x/s) * numpy.exp(-1.0*(x/s)**2/2.0)

Usually doubling the scaling parameter (also known as "level") of a wavelet halves its bandwidth. Plotting the FFT of the wavelet described above for different scales, s = 2**i, with i=1,2,3, ... the width is not halved for subsequent i.

Whats wrong with the morlet wavelet?

Upvotes: 1

Views: 3154

Answers (1)

MoonKnight
MoonKnight

Reputation: 23833

The above code that you have provided does not look (to me) as if it is properly constructing the Morlet wavelet. The paper A Practical Guide to Wavelet Analysis provides a great guide to the construction of Wavelet transforms and should provide an explanation to the effect of varying the wavelet scale.

Note, depending on your implementation, changing the wavelet scale will not update/change the scale of the FFT used to create the wavelet. Typically, the FFT is constructed, then it is used to construct the Descreet Wavelet Transform. Thus, changing the wavelet scale will not effect the underlying FFT.

I hope this helps.

Upvotes: 1

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