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Gabor transform/wavelet vs. Morlet wavelet

Started by Edward Jensen December 26, 2009
Dear all.

I am a little confused about the difference between the Gabor and the Morlet 
wavelet. As I have understood it the Gabor transform is a version of the 
STFT with a Gaussian window function. The different "Gaborlettes" are then 
created by translating and modulating the mother Gabor function but the 
Gaussian window has fixed width over all frequencies.

I the litterature the term Gabor wavelet turns up as a modified Gabor 
transform by depending the envelope with on the frequency. The Gabor 
wavelets are then generated by translation and dilation of the mother 
wavelet thus generating a wavelet frame. To me this looks and sounds very 
much  like the Morlet wavelet.

Is that correct or can anyone explain the different between the Gabor and 
the Morlet wavelets?

Thanks in advance and happy hollidays.
Edward. 


On 26 Des, 18:02, "Edward Jensen" <edw...@jensen.invalid> wrote:
> Dear all. > > I am a little confused about the difference between the Gabor and the Morlet > wavelet. As I have understood it the Gabor transform is a version of the > STFT with a Gaussian window function. The different "Gaborlettes" are then > created by translating and modulating the mother Gabor function but the > Gaussian window has fixed width over all frequencies.
The Gabor transform is a set of fixed-width Gaussian-shaped bandpass filters. Any filter bank can be implemented in either frequency or time domains, but the Gabor filters are probably easier to implement in frequency domain.
> I the litterature the term Gabor wavelet turns up as a modified Gabor > transform by depending the envelope with on the frequency. The Gabor > wavelets are then generated by translation and dilation of the mother > wavelet thus generating a wavelet frame. To me this looks and sounds very > much &#2013266080;like the Morlet wavelet.
This sounds like mumbo-jumbo to me. Again, the Gabor transform is a trivial filter bank. If somebody wants to implement a constant-Q version, then they might by all means do that, but it is still a filter bank.
> Is that correct or can anyone explain the different between the Gabor and > the Morlet wavelets?
Wavelets are little more than glorified filter banks. There is a little bit more to it (like scale relations and constant-Q properties), but not much. As with filter banks, one can use any number of basic designs; the Gaussian of the Gabor transform being one version, Morelet and Daubechies bases being others. Rune
On Dec 26 2009, 11:02&#2013266080;am, "Edward Jensen" <edw...@jensen.invalid>
wrote:
> Dear all. > > I am a little confused about the difference between the Gabor and the Morlet > wavelet. As I have understood it the Gabor transform is a version of the > STFT with a Gaussian window function. The different "Gaborlettes" are then > created by translating and modulating the mother Gabor function but the > Gaussian window has fixed width over all frequencies. > > I the litterature the term Gabor wavelet turns up as a modified Gabor > transform by depending the envelope with on the frequency. The Gabor > wavelets are then generated by translation and dilation of the mother > wavelet thus generating a wavelet frame. To me this looks and sounds very > much &#2013266080;like the Morlet wavelet. > > Is that correct or can anyone explain the different between the Gabor and > the Morlet wavelets? > > Thanks in advance and happy hollidays. > Edward.
Edward, If I remember correctly (it's been a while, so don't quote me) the Gabor wavelet uses a "true" gaussian as the multiplier, i.e. the form of exp(-x^2/2*sigma^2), while the Morlet wavelet uses just exp(-kx^2), not a "true" gaussian. Maurice Givens