DocumentCode :
916969
Title :
On the survival of sequence information in filters (Corresp.)
Author :
Golomb, Solomon W.
Volume :
18
Issue :
2
fYear :
1972
fDate :
3/1/1972 12:00:00 AM
Firstpage :
310
Lastpage :
312
Abstract :
Given a binary data stream 
and a filter 
whose output at time 
is 
for some complex 
, there are at most 
distinct values of 
. These values are the sums of the subsets of 
. It is shown that all 
sums are distinct unless 
is a unit in the ring of algebraic integers that satisfies a polynomial equation with coefficients restricted to +1, -1, and 0. Thus the size of the state space 
is if is transcendental, if 
is rational, and if is irrational algebraic but not a unit of the type mentioned. For the exceptional values of , it appears that the size of the state space grows only as a polynomial in if 
, but as an exponential 
with 
if 
.
and a filter whose output at time is for some complex , there are at most distinct values of . These values are the sums of the subsets of . It is shown that all sums are distinct unless is a unit in the ring of algebraic integers that satisfies a polynomial equation with coefficients restricted to +1, -1, and 0. Thus the size of the state space is if is transcendental, if is rational, and if is irrational algebraic but not a unit of the type mentioned. For the exceptional values of , it appears that the size of the state space grows only as a polynomial in if , but as an exponential with if .Keywords :
Filtering; Sequences; Binary sequences; Computer aided software engineering; Delta modulation; Equations; Information filtering; Information filters; Intersymbol interference; Low pass filters; Polynomials; State-space methods;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1972.1054762
Filename :
1054762
Link To Document :
