Continuous wavelet transform using derivative of Gaussian(DOG) wavelet

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

Answer 1

[David Ding]

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]

Hi,

Thank you very much for your answer. When I type

help cwtft

I get the following message:cwtft not found.

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.