Digital Signal Processing Reference
In-Depth Information
Figure 2.16 Representing a multidimensional vector
or company; the financial stability of a bank; and so on. The problem is to compare
these multivariate functions by making judgements about their maxima or minima.
In this context, understanding the n-dimensional vector gives a better solution to
the problems. Control engineers and statisticians
½
7
have used these functions
extensively.
Consider a multivariate function y
k
¼
f
ðx
k
;
u
k
Þ
where
x
k
is a multidimensional
vector and u is the input. This function describes a system. There are many times we
need to drive the given system in a specific trajectory in a multidimensional space,
subject to some conditions.
A digital filter defined in (2.23) and (2.24) is the best example of such functions
and is written like this:
w
k
¼ Aw
k
z
1
y
k
¼ C
t
w
k
z
1
þ B
u
k
and
þ D
u
k
:
2.6.3 System of Equations
Another example of a multivariate function is a system of simultaneous equations.
For the sake of brevity and comprehension, let us consider the following equations.
Equations of this type are encountered in different ways in many applications. Pay
attention to this subsection and it will give you a good insight into many solutions.
0
@
1
A
0
@
1
A
0
5
8
6
32
0
34
5
0
63
5
49
26
101
¼
9
x
1
x
2
;
ð
2
:
30
Þ
5
3
4
4
8
9
9
8
Ax ¼ y:
ð
2
:
31
Þ
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