L2330
DEVICES INCORPORATED
Coordinate Transformer
step resolution on a 24-bit internal
processor is 1 unit in the x and y thus
resulting in greater accuracy.
The minimum theoretical angle resolu-
tion that could be produced is 0.00175°
when x = 7FFFH and y = 1H. A 16-bit
internal processor can produce a
minimum angle resolution of only
0.00549° and will not be able to prop-
erly calculate the theoretical minimum
angle resolution. On the other hand, a
24-bit internal processor can produce a
minimum angle resolution of 0.00002°
and could therefore properly calculate
the theoretical minimum angle resolu-
tion.
Circle Test
When performing a polar-to-rectangu-
lar transformation, a 24-bit internal
processor proves to be significantly
more accurate than a 16-bit internal
processor.
In this study, we compare how accu-
rately a coordinate transformer with a
16-bit internal processor versus a 24-bit
internal processor can calculate all the
coordinates of a circle. By setting the
radius to 7FFFH (maximum before
overflow),
θ
is incremented using the
accumulator of the L2330 in steps of
0000 4000H until all the points of a full
circle are calculated into rectangular
coordinates.
The resulting rectangular coordinates
were plotted and graphed. A graphical
representation of the resulting vectors
for both 16-bit and 24-bit internal
processors are compared near 45°.
Theoretically, a perfect circle is the
desired output but when the resulting
vectors from a coordinate transformer
with 16-bit internal processor are
graphed and displayed as shown in
Figure 3, we see significant errors due
to the inherent properties of a digital
coordinate transformation system. In
comparison, the 24-bit internal proces-
sor proves to be significantly more
accurate than a 16-bit internal processor
due to minimization of truncation
errors. In many applications, this
margin of error is of great significance
especially when being used in applica-
tions such as medical ultrasound or
modulation techniques.
Data values for Figure 3 and Figure 4
are shown in Table 4. By looking at
these values, we observe the step
resolution on a 16-bit internal processor
is not 1 unit in the x and y. In most
cases, the minimum step resolution is 2
units in the x and y. On the other hand,
F
IGURE
3. C
IRCLE
T
EST
R
ESULT
N
EAR
45° (16-B
IT
I
NTERNAL
P
ROCESSOR
)
23200
23190
23180
Y
23170
23160
23150
23140
23140
23150
23160
23170 23180
23190
23200
X
F
IGURE
4. C
IRCLE
T
EST
R
ESULT
N
EAR
45° (24-B
IT
I
NTERNAL
P
ROCESSOR
)
23200
23190
23180
Y
23170
23160
23150
23140
23140
23150
23160
23170 23180
23190
23200
X
Special Arithmetic Functions
7
09/27/2001–LDS.2330-E
LOGIC [ LOGIC DEVICES INCORPORATED ]
