Digital Signal Processing Reference
In-Depth Information
be equal to the
R
TX
value of 1 from run 2, and so on. To carry out the least
squares fit, we put the observations from the table into the coded input matrix
(
X
) and response vectors (
y
eyeH
and
y
eyeW
). Note that the eye height and width
are expressed in units of mV and ps, respectively.
1
x
1
,
1
x
2
,
1
···
x
20
,
1
1
x
1
,
2
x
2
,
2
···
x
20
,
2
X
=
(14-8)
.
.
.
.
.
.
.
1
x
1
,
28
x
2
,
28
···
x
20
,
28
With the observations in matrix form, application of the model fitting equations
=
(
X
T
X
)
−
1
X
T
y
eyeH
b
eyeH
(14-9)
=
(
X
T
X
)
−
1
X
T
y
eyeW
b
eyeW
(14-10)
gives the estimated fit coefficient vectors:
95
.
51799
2
.
32444
0
.
12056
9
.
55222
89
.
10651
−
1
.
94444
0
.
55556
−
0
.
44444
−
30
.
81556
−
−
10
.
83333
−
0
.
28778
0
.
18751
7
.
05556
−
0
.
13314
−
2
.
18063
−
0
.
56250
0
.
36686
1
.
18750
−
1
.
19749
1
.
26063
b
eyeH
=
−
2
.
43813
b
eyeW
=
−
1
.
56250
0
.
36686
−
0
.
44249
−
3
.
88563
−
1
.
93750
0
.
56250
0
.
31250
−
0
.
02937
−
4
.
43812
−
−
2
.
97249
4
.
13314
−
1
.
77437
0
.
22937
−
1
.
56250
1
.
43750
−
2
.
11688
−
0
.
56250
−
20
.
42063
−
8
.
93750
−
14
.
61249
−
8
.
13314
Before proceeding further, it makes sense that we should apply the estimated
fit coefficients,
b
eyeH
and
b
eyeW
, to the input observed using equation (14-6) to
obtain estimates of the response. These estimates are shown in columns (9) and
(10) of Table 14-3. Comparing the predicted and observed responses, we see that
our models agree to within approximately
±
4mVand
±
4 ps.
Search WWH ::
Custom Search