Description
Return ideal zero-order-hold frequency factors.
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 ideal zero-order-hold frequency factors.
When to use this tool
Use Sample Hold Phase Delay Factor when checking one supplied sample, delay or quantization convention.
How to use the tool and how it works
- Enter frequencyHz, sampleSeconds. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read phaseRadians, equivalentDelay, sincFactor. Use the output convention below.
Return ideal zero-order-hold frequency factors. Require frequencyHz >= 0 and sampleSeconds > 0; phaseRadians = -pi*f*T, equivalentDelay = T/2, sincFactor = sin(pi*f*T)/(pi*f*T), using one at zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| frequencyHz | Frequency in cycles per second (Hz); angular factors include 2*pi. | Required. Finite number; minimum 0. |
| sampleSeconds | Sample interval in seconds; strictly positive. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| phaseRadians | Unwrapped -pi*f*T linear-delay factor; outside the first lobe it is not the full phase of the signed transfer factor. Unit: rad. | Required. Finite number. |
| equivalentDelay | Equivalent Delay | Required. Finite number. |
| sincFactor | sin(pi*f*T)/(pi*f*T), including its sign; one at zero frequency. | Required. Finite number. |
{
"input": {
"frequencyHz": 1,
"sampleSeconds": 0.5
},
"output": {
"phaseRadians": -1.5707963267948966,
"equivalentDelay": 0.25,
"sincFactor": 0.6366197723675814
}
}Limitations and assumptions
- The sinc factor is signed and unnormalized phase follows this factorization; aliasing and a complete sampled loop are not modeled.
- 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
- Sample Hold Delay Phase Sign
Return delay phase under an explicit exponential convention.
- Sample Delay Phase Reference Gap
Compare sample-delay phase with a reference.