Description
Return scaled quantization half-width and conditional uniform standard deviation.
Sampled control models distinguish physical delay, held-state age, phase convention and quantization. A local frequency factor or error envelope assumes the stated sample and signal model, rather than measuring actual sensor or plant behavior.
Return scaled quantization half-width and conditional uniform standard deviation.
When to use this tool
Use Sensor Quantization Equivalent Error Term when checking one supplied sample, delay or quantization convention.
How to use the tool and how it works
- Enter stepSize, gain. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read outputHalfWidth, outputUniformSd. Use the output convention below.
Return scaled quantization half-width and conditional uniform standard deviation. Require stepSize >= 0; outputHalfWidth = abs(gain)*step/2 and outputUniformSd = abs(gain)*step/sqrt(12).1
A uniform error over a full-width interval has standard deviation equal to width/sqrt(12). This requires an explicit distribution assumption, not merely a resolution specification.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| stepSize | Step Size | Required. Finite number; minimum 0. |
| gain | Gain | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| outputHalfWidth | Output Half Width | Required. Finite number. |
| outputUniformSd | abs(gain)*stepSize/sqrt(12), assuming uniform quantization error. | Required. Finite number. |
{
"input": {
"stepSize": 2,
"gain": 3
},
"output": {
"outputHalfWidth": 3,
"outputUniformSd": 1.7320508075688774
}
}Limitations and assumptions
- The SD assumes uniform quantization error; actual noise, bias and gain validity are not established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a validated sampled-system and measurement model for practical control design, operating limits and safety.
References
Similar or alternative tools
- Sensor Quantization Error Halfband
Return a biased quantization-error band after supplied scaling.
- Error Integral Leakage One Step
Update a leaking integral state with an error increment.