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NOTATION
Thisisalistofsymbolsandacronymswhichmayappearinmorethanonechapterofthistextbook.The
“local”notationisdefinedintherelevantchapters.
Commonnumbersets
N
Z
R
R
C
+
–setofnaturalnumbers;
–setofintegernumbers;
–setofrealnumbers;
–setofpositiverealnumbers;
–setofcomplexnumbers.
Basicvariables
x
y
f|
()
t
h
N
t
8
n
n
ω
s
z
–general-purposeindependentvariable,
yEY
xEX
;
;
–general-purposedependentvariable,
–general-purposefunction,mostoften:
y
±
fx
()
;
–independentvariable,mostoftenmodellingtime,
t
E
[0,];
T
–stepofdiscretisationforindependentvariablesxandt;
–numberofdiscretisationsteps;
–n-thpointofdiscretisation:
t
n
±
t
0
+∆for
nt
n
±
0,1,...,
N
–
1;
–relativeerrorcorruptingdataduetotheirfloating-pointrepresentation,briefly:representa-
tionerror;
–relativeerrorcorruptingtheresultofafloating-pointoperation,briefly:roundingerror;
–argumentoftheFouriertransform,briefly:pulsation;
–argumentoftheLaplacetransform,briefly:complexpulsation;
–argumentoftheLaurenttransform(calledalsoZ-transform).
Rulesforgenerationandmodificationofbasicvariables
x
-
x
~
x
ˆ
x
x
T
X
X
T
–error-freeversionofascalarvariablex(thedotmaybeomittedifthecontextisexcluding
ambiguity);
–error-corruptedversionofx;
–estimateofx(aspecialcaseofx
~);
columnvectorofhomogenousscalarvariables
x(nEZ),e.g.
n
x
=||
f1
||
x
x
1
2
;
–
||
LJ
x
3
–transposedvectorx;
–rectangularmatrixofhomogenousscalarvariables
x
nm
,
,e.g.
X
=|
f
L
x
x
1,1
2,1
x
x
1,2
2,2
x
x
2,3
1,3
1
|
J
;
–transposedmatrixX;
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