For Gabor sets, (g; a, b), it is known that (g; a, b) is a frame if and only if (g; 1/b, 1/a) is a Riesz basis for its span. In particular, for every g there is a0 such that for every a < a0, there is a bm = bm(a) > 0 so that for every b < bm, (g; a, b) is a frame, and (g; 1/b, 1/a) is a Riesz basis sequence. In this talk we shall consider a similar problem for wavelet sets (Ψ; a, b). The main ...

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g -frames. In this paper we introduce frames of submodules, fusion frames and g -frames in Hilbert C∗ -modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g -frames in Hilbert spaces.

Let (gna,mb)n,m∈Z be a Gabor frame for L (R) for given window g. We show that the window h0 = S− 1 2 g that generates the canonically associated tight Gabor frame minimizes ‖g − h‖ among all windows h generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in ...

A Weyl-Heisenberg frame for L2(R) is a frame consisting of modulates Embg(t) = e 2πimbtg(t) and translates Tnag(t) = g(t − na), m,n ∈ Z, of a fixed function g ∈ L2(R), for a, b ∈ R. A fundamental question is to explicitly represent the families (g, a, b) so that (EmbTnag)m,n∈Z is a frame for L2(R). We will show an interesting connection between this question and a classical problem of Littlewoo...

The limited bandwidth of sensor-based feedback control, restricts the execution speed of a force controlled planar contour following task if the shape of the workpiece is unknown. This paper shows how appropriate feedforward control of the task frame orientation, calculated on-line from an eye-in-hand camera image, results in a faster or more accurate executed task. However, keeping the contour...

This paper is an investigation of shift invariant subspaces of L2(G), where G is a locally compact abelian group, or in general a local field, with a compact open subgroup. In this paper we state necessary and sufficient conditions for shifts of an element of L2(G) to be an orthonormal system or a Parseval frame. Also we show that each shift invariant subspace of L2(G) is a direct sum of princi...

Given certain compactly supported functions g ∈ L2(Rd) whose Zd-translates form a partition of unity, and real invertible d×d matrices B, C for which ||CT B|| is sufficiently small, we prove that the Gabor system {EBmTCng}m,n∈Zd forms a frame, with a (non-canonical) dual Gabor frame generated by an explicitly given finite linear combination of shifts of g. For functions g of the above type and ...

Agregation With Fragment Retransmision (AFR) is a frame transmission scheme that can improve the efficiency and the throughput of MAC layer in WLAN 802.11n. In this paper, we studied the performance of AFR scheme when various VoIP and video traffics transmitted over WLAN. The purpose of this work is to know how the number of connections, packet size and fragment size of VoIP and video traffics ...