ON HILBERT TRANSFORM OF GABOR AND WILSON SYSTEMS
2014 ◽
Vol 12
(02)
◽
pp. 1450012
◽
Keyword(s):
Given that the Gabor system {EmbTnag}m,n∈ℤ is a Gabor frame for L2(ℝ), a sufficient condition is obtained for the Gabor system {EmbTnaHg}m,n∈ℤ to be a Gabor frame, where Hg denotes the Hilbert transform of g ∈ L2(ℝ). It is proved that the Hilbert transform operator and the frame operator for the Gabor Bessel sequence {EmbTnag}m,n∈ℤ commute with each other under certain conditions. Also, a sufficient condition is obtained for the Wilson system [Formula: see text] to be a Wilson frame given that [Formula: see text] is a Wilson frame. Finally, we obtain conditions under which the Hilbert transform operator and the frame operator for the Wilson Bessel sequence [Formula: see text] commute with each other.
2020 ◽
Vol 2020
(48)
◽
pp. 17-24
Keyword(s):
2009 ◽
Vol 52
(3)
◽
pp. 507-510
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2015 ◽
Vol 2015
◽
pp. 1-3
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1968 ◽
Vol AES-4
(5)
◽
pp. 802-802
Keyword(s):