Gabor Frames in and Linear Dependence
O Christensen, M Hasannasab - Journal of Fourier Analysis and …, 2019 - Springer
Journal of Fourier Analysis and Applications, 2019•Springer
We prove that an overcomplete Gabor frame in ℓ^ 2 (Z) ℓ 2 (Z) generated by a finitely
supported sequence is always linearly dependent. This is a particular case of a general
result about linear dependence versus independence for Gabor systems in ℓ^ 2 (Z) ℓ 2 (Z)
with modulation parameter 1/M and translation parameter N for some M, N ∈ N, M, N∈ N,
and generated by a finite sequence g in ℓ^ 2 (Z) ℓ 2 (Z) with K nonzero entries.
supported sequence is always linearly dependent. This is a particular case of a general
result about linear dependence versus independence for Gabor systems in ℓ^ 2 (Z) ℓ 2 (Z)
with modulation parameter 1/M and translation parameter N for some M, N ∈ N, M, N∈ N,
and generated by a finite sequence g in ℓ^ 2 (Z) ℓ 2 (Z) with K nonzero entries.
Abstract
We prove that an overcomplete Gabor frame in generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in with modulation parameter 1 / M and translation parameter N for some and generated by a finite sequence g in with K nonzero entries.
Springer
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