ISSN:
1531-5851
Keywords:
42C15
;
Weyl-Heisenberg frame
;
dual window
;
spline
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We present a simple proof of Ron and Shen's frame bounds estimates for Gabor frames. The proof is based on the Heil and Walnut's representation of the frame operator and shows that it can be decomposed into a continuous family of infinite matrices. The estimates then follow from a simple application of Gershgorin's theorem to each matrix. Next, we show that, if the window function has exponential decay, also the dual function has some exponential decay. Then, we describe a numerical method to compute the dual function and give an estimate of the error. Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01257190
