DocumentCode :
924075
Title :
Best asymptotic bounds for truncation error in sampling expansions of band-limited signals (Corresp.)
Author :
Piper, Harvey S., Jr.
Volume :
21
Issue :
6
fYear :
1975
fDate :
11/1/1975 12:00:00 AM
Firstpage :
687
Lastpage :
690
Abstract :
For band-limited functions with finite energy, it is known that bounds on the truncation error incurred when the function is approximated by 2N + 1 terms in the cardinal expansion can be obtained that go to zero like N^{-1/2} . If the additional restriction is made that a guard band is present (that is, the function is sampled faster than the minimum rate), then bounds can be obtained that go to zero like N^{-1} , both for finite energy functions and for functions having absolutely integrable Fourier transforms. It is shown here that these bounds are all asymptotically the best possible. It is also shown that, in the absence of a guard band, bund-limited functions with absolutely integrable Fourier transforms exist for which the truncation error goes to zero arbitrarily slowly.
Keywords :
Band-limited signals; Signal sampling/reconstruction; Additive noise; Equalizers; Error analysis; Finite wordlength effects; Fourier transforms; Gaussian noise; Intersymbol interference; Jitter; Sampling methods; Upper bound;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1975.1055453
Filename :
1055453
Link To Document :
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