Gabor frames with trigonometric spline dual windows
نویسندگان
چکیده
منابع مشابه
Gabor Dual Spline Windows
An algorithm is presented for constructing dual Gabor window functions that are splines. The spline windows are supported in [−1, 1], with a knot at x = 0, and can be taken C smooth and symmetric. The translation and modulation parameters satisfy 0 < ab ≤ 1/2. The full range 0 < ab < 1 is handled by introducing an additional knot. Many explicit examples are found.
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We present an application of the dual Gabor frames to image processing. Our algorithm is based on finding some dual Gabor frame generators which reconstructs accurately the elements of the underlying Hilbert space. The advantages of these duals constructed by a polynomial of Gabor frame generators are compared with their canonical dual.
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we present an application of the dual gabor frames to image processing. our algorithm is based on finding some dual gabor frame generators which reconstructs accurately the elements of the underlying hilbert space. the advantages of these duals constructed by a polynomial of gabor frame generators are compared with their canonical dual.
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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 ...
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Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...
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ژورنال
عنوان ژورنال: Asian-European Journal of Mathematics
سال: 2015
ISSN: 1793-5571,1793-7183
DOI: 10.1142/s1793557115500722