We provide explicit constructions of particularly convenient dual pairs of Gabor frames. We prove that arbitrary polynomials restricted to sufficiently large intervals will generate Gabor frames, at least for small modulation parameters. Unfortunately, no similar function can generate a dual Gabor frame, but we prove that almost any such frame has a dual generated by a B-spline. Finally, for fr...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

in a novel dual bed reactor fischer-tropsch synthesis was studied by using two diffrent cobalt catalysts. an alkali-promoted cobalt catalyst was used in the first bed of a fixed-bed reactor followed by a rutenuim promoted cobalt catalyst in the second bed. the activity, product selectivity and accelerated deactivation of the system were assessed and compared with a conventional single bed react...

We study sparsity and spectral properties of dual frames of a given finite frame. We show that any finite frame has a dual with no more than n2 non-vanishing entries, where n denotes the ambient dimension, and that for most frames no sparser dual is possible. Moreover, we derive an expression for the exact sparsity level of the sparsest dual for any given finite frame using a generalized notion...

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

Standard video coders often use the immediate past frame as a reference frame with motion compensation for video encoding. In this paper, we use dual reference frame motion compensation in the context of high bandwidth to low bandwidth switching such as from an Ethernet connection to a GPRS system. The implementation is based on MPEG-4. Simulation results show that there is a significant gain i...

Standard video coders often use the immediate past frame as a reference frame with motion compensation for video encoding. In this paper, we use dual reference frame motion compensation in the context of high bandwidth to low bandwidth switching such as from an Ethernet connection to a GPRS system. The implementation is based on MPEG-4. Simulation results show that there is a significant gain i...

where A and B are called the lower frame bound and upper frame bound, respectively. In particular, when A= B = 1, we say that {hk}k∈Z is a (normalized) tight frame in H. The 1 Research was partially supported by NSF Grants DMS-9872890, DMS-9706753 and AFOSR Grant F4962098-1-0044. Web: http://www.princeton.edu/~icd. 2 Research was supported by NSERC Canada under Grant G121210654 and by Alberta I...

In this paper, we present simulation results for the performance gain of smart dual antennas at handsets for the forward link in the cdma2000 system. The system was modeled with the SPW of Cadence. Three types of the channel model, two levels of diversity combining, and three diversity combining schemes were investigated. Our simulation results show that the average performance gain (reduction ...