# gabor wavelet and gabor transform

I was reading a paper 'A Flexible Framework for Local Phase Coherence Computation' (paper URL) on using wavelets for local phase coherence. I just want to be sure. Is the gabor wavelet the same as the gabor function in the gabor transform (STFT)? If not, can we use a Windowed Fourier Transform instead?

## 1 Answer

The Gabor wavelet is (almost) the same as the Morlet wavelet (some authors distinguish these two by an additional constant to fulfill the wavelet's admissibility condition). And yes, it is the same function as in the Gabor transform (gaussian windowed oscillation).

The application of phase coherence should be independent of the underlying wavelet and the nature of the transform (Wavelet, Gabor/STFT, other weird metrics). Essentially important is the concept of reproducing kernels and the intrinsic (Heisenberg) uncertainty that influence you measure of phase coherence and must be taken care of.

• Hi, is it possible for you to write down the formula for Gabor wavelet/Gabor transform(STFT)? – meta_warrior Jan 15 '14 at 9:28
• @André Uhhh... almost ? Unless otherwise specified the Morlet is real valued whereas the Gabor - complex. – Sektor Jan 15 '14 at 10:21
• @Sektor: What is your view on the question above? – meta_warrior Jan 15 '14 at 10:35
• Generally, speaking - yeah, they are the same. But not if we speak strictly - there are noticeable differences between the two and also the Gabor function is different from what you want it to be, i.e. the part that we integrate in the STFT, that is actually a complex exponential multiplied by a Gaussian function :) – Sektor Jan 15 '14 at 10:45
• Again if we loosen up - they are the same :) – Sektor Jan 15 '14 at 10:46