Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...

A new signal processing method is presented for the suppression of intermittent clutter echoes in radar wind profilers. The technique presented makes use of a discrete Gabor frame expansion in combination with a statistical significance test. The rationale of this algorithm is outlined and an example using data obtained with an operational 482 MHz wind profiler is given.

The main contribution of this paper is twofold. First, some new sufficient conditions, under which the shift-invariant system is a frame for L(R), were established. Second, those sufficient conditions are used to obtain some new results about Gabor frames. 2000 Mathematics Subject Classification. 42C15, 42C40.

We study the structure of operators from the Schwartz space S (R) into the tempered distributions S (R) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor and wavelet frames.

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

Abstract We consider Gabor frames generated by a general lattice and window function that belongs to one of the following spaces: Sobolev space $$V_1 = H^1(\mathbb {R}^d)$$ V 1 = H ( R</mml...

The Fourier transform has been a major tool in analysis for over 100 years. However, it solely provides frequency information, and hides (in its phases) information concerning the moment of emission and duration of a signal. D. Gabor resolved this problem in 1946 [93] by introducing a fundamental new approach to signal decomposition. Gabor’s approach quickly became the paradigm for this area, b...

This paper describes a new motion estimation algorithm which is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable 2-d Discrete Wavelet Transform (DWT) on each frame to eeciently construct a multiresolution pyramid of subimages. The DWT is based on a complex-valued pair of 4-tap FIR lters with Gabor-like characteris...

Direction discrimination (upward/downward or left/right) for a Gabor patch in a two-frame motion display was measured as a function of the inter-frame displacement size of the component grating with the stimulus position (center, left, right, upper and lower visual fields) as a parameter. The results showed that, for vertical motion in the center, left, right and lower visual fields, the observ...

We describe a method for local time-adaptation of the spectrogram of audio signals: it is based on the decomposition of a signal within a Gabor multi-frame of raised cosine windows through the STFT operator. The sparsity of the analyses in every single frame of the multiframe is evaluated through the Rényi entropies measures. We give an analytical expression for the entropy of the spectrogram o...