Varying the time-frequency lattice of Gabor frames

Varying the Time-frequency Lattice of Gabor Frames

A Gabor or Weyl-Heisenberg frame for L2(Rd) is generated by time-frequency shifts of a square-integrable function, the Gabor atom, along a time-frequency lattice. The dual frame is again a Gabor frame, generated by the dual atom. In general, Gabor frames are not stable under a perturbation of the lattice constants; that is, even for arbitrarily small changes of the parameters the frame property...

time-varying deconvolution operator in gabor domain

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Density of Gabor Frames

Deformations of Gabor Frames

The quantum mechanical harmonic oscillator Hamiltonian H = (t − ∂ t )/2 generates a one–parameter unitary group W (θ) = e in L(R) which rotates the time–frequency plane. In particular, W (π/2) is the Fourier transform. When W (θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one–parameter family of ...

Time-frequency structured decorrelation of speech signals via nonseparable Gabor frames

We present a new approach to the linear representation of speech signals that combines desirable structure, computational e ciency and almost decorrelation. The basic principle is a statistically adapted, group{theoretical modi cation of the classical Gabor expansion. In contrast to traditional linear time{frequency (TF) representations which always correspond to a separable tiling of the TF pl...