L2330 View Datasheet(PDF) - LOGIC Devices
Part Name
Description
MFG CO.
'L2330' PDF : 14 Pages View PDF
DEVICES INCORPORATED
L2330
Coordinate Transformer
Internal Precision
When performing a coordinate
transformation, inaccuracies are
introduced by a combination of
quantization and approximation
errors. The accuracy of a coordinate
transformer is dependent on the
word length used for the input
variables, the word length used for
internal calculations, as well as the
number of iterations or steps per-
formed. Truncation errors are due
to the finite word length, and
approximation errors are due to the
finite number of iterations. For
example, in the case of performing a
polar-to-rectangular transformation,
the accuracy of the rotation will be
determined by how closely the input
rotation angle was approximated by
the summation of sub-rotation
angles.
In this study, we examine the
effectiveness of 16-bit internal
precision versus 24-bit internal
precision. 10,000 random Rectangu-
lar coordinates were converted to
Polar and back to Rectangular. The
resulting Rectangular coordinates
from this double conversion were
then compared to the original
Rectangular coordinates input to the
device. These vectors, with maxi-
mum word width of 16-bits, were
sent through a 16-bit internal
processor versus a 24-bit internal
processor. The Rectangular coordi-
nates were limited to the following
conditions:
–32769<x<32768
–32769<y<32768
Using the 16-bit internal processor, the
resulting Rectangular coordinates were
compared to the original Rectangular
coordinates (see Table 3). Using the 24-
bit internal processor, the resulting
Rectangular coordinates were com-
pared to the original Rectangular
coordinates (see Table 3). By way of
comparison between the 16-bit internal
processor and the 24-bit internal
processor, we find that the 24-bit
internal processor is significantly more
accurate. This accuracy is due to
internal word length. During coordi-
nate transformation, the number of bits
truncated within a 24-bit internal
processor are much smaller than in a
16-bit internal processor resulting in
smaller error.
TABLE 3. DOUBLE CONVERSION ERROR
Error
Internal 16-bit
Mean Error (X)
Mean Error (Y)
Mean Absolute Error (X)
0.0216
–0.0036
1.5736
Mean Absolute Error (Y)
1.0756
Root Mean Square Error (X)
Root Mean Square Error (Y)
Max Error (X)
2.0168
1.4356
6.0/–7.0
Max Error (Y)
Standard Deviation of Error (X)
Standard Deviation of Error (Y)
5.0/–5.0
2.0168
1.4357
Internal 24-bit
–0.0118
–0.0028
0.5116
0.5160
0.7664
0.7738
3.0/–3.0
3.0/–3.0
0.7664
0.7739
Special Arithmetic Functions
6
09/27/2001–LDS.2330-E
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