Note on B-splines, wavelet scaling functions, and gabor frames
نویسندگان
چکیده
منابع مشابه
Note on B-splines, wavelet scaling functions, and Gabor frames
Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and time-shift and frequency-shift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3, . . . and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wa...
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We study totally positive (TP) functions of finite type and exponential Bsplines as window functions for Gabor frames. We establish the connection of the Zak transform of these two classes of functions and prove that the Zak transforms have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on the variation-diminishing property of shifts of exponential B-splines....
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We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying ...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2003
ISSN: 0018-9448
DOI: 10.1109/tit.2003.820022