Continuous wavelet transform using derivative of Gaussian(DOG) wavelet
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I am trying to do continuous wavelet transform using a derivative of Gaussian order two wavelet. I want to obtain the frequencies and magnitude but cwt command doesn't seem to have DOG wavelet. Is it a way to perform continuous wavelet transform and acquire the frequencies with the specific filter?
Thank you very much in advance
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David Ding
il 25 Set 2017
Hi,
If I may assume you are using the "cwtft" function for your analysis, then DOG wavelet is one of the available wavelets that you may use. I see that the only way to access the documentation for this function is via the MATLAB Command Window. Nonetheless, you may do:
>> help cwtft
And the documentation appears. In particular, this may be of relevance to you inside the doc:
CWTSTRUCT = cwtft(SIG,'scales',SCA,'wavelet',WAV) lets you
define the scales and the wavelet. Supported analyzing wavelets are:
'morl' - Morlet wavelet (analytic)
'morlex' - Morlet wavelet (nonanalytic)
'morl0' - Exact zero-mean Morlet wavelet (nonanalytic)
'bump' - Bump wavelet (analytic)
'paul' - Paul wavelet (analytic)
'dog' - N-th order derivative of Gaussian (nonanalytic)
'mexh' - Second derivative of Gaussian (nonanalytic)
See the help for CWTFTINFO for definitions of the supported wavelets
and their default parameter values.
If you type:
>> cwtftinfo
In one of the sections, you get more details about the DOG wavelet:
DOG:
'dog': m order Derivative Of Gaussian
PSI_HAT(k) = -(i^m/sqrt(gamma(m+0.5)))(k^m)exp(-k^2/2)
Parameter: m (order of derivative), default m = 2. The order
m must be even.
sqrt(m+1/2) is the approximate center frequency in radians/sample.
The center frequency cycles/sample is sqrt(m+1/2)/(2*pi).
'mexh':
PSI_HAT(k) = (1/gamma(2+0.5))k^2 exp(-k^2/2)
(DOG wavelet with m = 2)
sqrt(5/2) is the approximate center frequency in radians/sample.
The center frequency is cycles/sample is sqrt(5/2)/(2*pi).
Thanks,
David
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