# Continuous wavelet transform using derivative of Gaussian(DOG) wavelet

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Efstathios Kontolatis on 18 Sep 2017
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

David Ding on 25 Sep 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
Efstathios Kontolatis on 2 Oct 2017
Hi,
help cwtft
Use the Help browser search field to search the documentation, or type "help help" for help command options, such as help for methods.
For your information I use MATLAB R2016b.
Thank you again your assumption is correct about what I want to use.