DocumentCode :
916514
Title :
Sampling series for band-limited generalized functions
Author :
Pfaffelhuber, Ernst
Volume :
17
Issue :
6
fYear :
1971
fDate :
11/1/1971 12:00:00 AM
Firstpage :
650
Lastpage :
654
Abstract :
For an arbitrary band-limited generalized function 
a representation is obtained that is a combination of a Taylor series and a conventional sampling series. A parameter 
that enters can be chosen such as to make the series rapidly convergent. Furthermore, it is shown that, for suitably restricted test functions, can be represented by a conventional sampling series and by a series of delta functions with weights equal to the sampling values. The results apply also to ordinary band-limited functions.
a representation is obtained that is a combination of a Taylor series and a conventional sampling series. A parameter that enters can be chosen such as to make the series rapidly convergent. Furthermore, it is shown that, for suitably restricted test functions, can be represented by a conventional sampling series and by a series of delta functions with weights equal to the sampling values. The results apply also to ordinary band-limited functions.Keywords :
Band-limited signals; Generalized functions; Signal sampling/reconstruction; Bandwidth; Channel capacity; Fourier transforms; Information rates; Linear systems; Sampling methods; Taylor series; Terrorism; Testing; Transfer functions;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1971.1054716
Filename :
1054716
Link To Document :
