We discuss a new transform, called the empirical Gabor transform, based on the empirical wavelet transform first introduced by Gilles in 2013. The empirical Gabor transform can be seen as an adaptive filterbank, a compromise between the empirical mode decomposition and the Gabor transform. In the original construction, the empirical wavelet transform uses Meyer type wavelets and only considers real signals in a discrete setting. In this thesis, we use the dilation D[subscript an], translation T[subscript wn] , and modulation E_[subscript b] of a gaussia window ψ(ξ) in the Fourier domain to construct an empirical Gabor system {E_ [subscript b]T[subscript wn]D[subscript an]ψ}b ∈,R,n ∈N with which we can define the continuous empirical Gabor transform of a complex or real signal. We extend this to the discrete case by introducing empirical Gabor frames, a special case of nonstationary Gabor frames developed by Balazs, et al. in 2011. We calculate the empirical Gabor transform of some example signals and compare to the empirical wavelet transform.
