TY - JOUR
T1 - Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions
AU - Christensen, O.
AU - Janssen, A.J.E.M.
AU - Kim, H.O.
AU - Kim, R.Y.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.
AB - It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.
KW - Almost perfect reconstruction
KW - Approximately dual frames
KW - Frames
KW - Gaussian
KW - Two-sided exponential
UR - http://www.scopus.com/inward/record.url?scp=85043691373&partnerID=8YFLogxK
U2 - 10.1007/s10444-018-9595-7
DO - 10.1007/s10444-018-9595-7
M3 - Article
AN - SCOPUS:85043691373
SN - 1019-7168
VL - 44
SP - 1519
EP - 1535
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
IS - 5
ER -