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L2330 Datasheet(PDF) 6 Page - LOGIC Devices Incorporated |
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L2330 Datasheet(HTML) 6 Page - LOGIC Devices Incorporated |
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6 / 14 page  DEVICES INCORPORATED L2330 Coordinate Transformer 6 Special Arithmetic Functions 09/27/2001–LDS.2330-E 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 Error Internal 16-bit Internal 24-bit Mean Error (X) 0.0216 –0.0118 Mean Error (Y) –0.0036 –0.0028 Mean Absolute Error (X) 1.5736 0.5116 Mean Absolute Error (Y) 1.0756 0.5160 Root Mean Square Error (X) 2.0168 0.7664 Root Mean Square Error (Y) 1.4356 0.7738 Max Error (X) 6.0/–7.0 3.0/–3.0 Max Error (Y) 5.0/–5.0 3.0/–3.0 Standard Deviation of Error (X) 2.0168 0.7664 Standard Deviation of Error (Y) 1.4357 0.7739 TABLE 3. DOUBLE CONVERSION ERROR 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. |
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