Digital Signal Processing Reference
In-Depth Information
Example E.2
Initialize the following matrix:
24
−
10
52
A
=
3 9
+
=(
A
T
A
)
−
1
A
T
with T denoting
and take the pseudo-inverse of
A
, defined as
A
the conjugate transpose operation.
Solution
The following M
ATLAB
code initializes matrix
A
:
>>A=[24-10;5239]; %Thesemicolon inside square
% parenthesis separates
% adjacent rows of a matrix
An alternative but longer set of instructions for the initialization of
A
is as
follows:
>> A(1,1)=2; A(1,2)=4; A(1,3)=-1; A(1,4)=0;
>> A(2,1)=5; A(2,2)=2; A(2,3)=-3; A(2,4)=9;
To calculate the pseudo-inverse of
A
, the following instruction may be used:
>> Ainverse = inv(A'*A)*A'; % Function inv calculates
% inverse of a matrix
% while ' denotes conjugate
% transpose
which returns a warning that the matrix is singular. From linear algebra, we
know that the inverse of a matrix only exits if it is non-singular, hence the
pseudo-inverse does not exist for the above choice of
A
.
Example E.3
Initialize the following discrete-time function:
π
15
f
[
k
]
=
2
∗
cos
∗
k
for
0
≤
k
≤
30
.
Solution
As in other high-level languages, we can use a
for
statement to initialize the
function
f
. The code is given by
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