Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of Gabor Frames   The quantum mechanical harmonic oscillator Hamiltonian generates a
one-parameter unitary group W(\theta) in L^2(R) which rotates the
time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When
W(\theta) 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 frames, which we call a deformation of the original.
For example, beginning with the usual tight frame F of Gabor wavelets generated
by a compactly supported window g(t) and parameterized by a regular lattice in
the time-frequency plane, one obtains a family of frames F_\theta generated by
the non-compactly supported windows g_\theta=W(theta)g, parameterized by
rotated versions of the original lattice. This gives a method for constructing
tight frames of Gabor wavelets for which neither the window nor its Fourier
transform have compact support. When \theta=\pi/2, we obtain the well-known
Gabor frame generated by a window with compactly supported Fourier transform.
The family F_\theta therefore interpolates these two familiar examples.

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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat