Digital Signal Processing Reference
In-Depth Information
5.3.4 Synchro-to-Digital Converters
It may seem odd to talk about synchro-to-digital (S/D) converters but a close look
indicates that they are functionally similar to A/D converters and offer an
interesting mathematical viewpoint. The position on a rotating system is uniquely
depicted as a 3-tuple
through a table. In simple terms it is a mapping function from
<
3
to
<
. This
is mathematically the same as finding a direction using an antenna system
(Section 6.2).
¼½
v
1
v
2
v
3
. This vector is mapped into a scalar as
!
H
H
5.4 Second-Order BPF
Suppose the following transfer function is to be realised in hardware. The block
schematic will be as shown in Figure 5.6.
0062z
2
0
:
0062
0
:
H
ð
z
Þ¼
9875z
2
:
ð
5
:
4
Þ
1
1
:
608z
1
þ
0
:
uk
0.0062
b1
+
+
×
+
+
+
xk
1.608
a1
×
p
4
p
1
−0.9875
a2
×
1
z
1
z
z1
z2
p
2
×
−0.0062
b2
p
3
Figure 5.6 SIMULINK implementation of a second-order filter
The above z-domain filter can be readily rewritten as difference equations in the
time domain:
w
k
¼
1
:
608w
k
1
0
:
9875w
k
2
þ
u
k
;
ð
5
:
5
Þ
x
k
¼
0
:
0062w
k
0
:
0062w
k
2
:
ð
5
:
6
Þ
This requires us to perform four multiplications and three additions. We can see that
not all the multiplications and additions are serial. The way we have written the
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