Sample Hold Delay Phase Sign Tool

Description

Return delay phase under an explicit exponential convention.

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 delay phase under an explicit exponential convention.

When to use this tool

Use Sample Hold Delay Phase Sign when checking one supplied sample, delay or quantization convention.

How to use the tool and how it works

Enter angularFrequency, delay, convention. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read phaseShift. Use the output convention below.

Return delay phase under an explicit exponential convention. Require delay >= 0 and convention exp-positive or exp-negative; phaseShift = -omega*delay or +omega*delay respectively.^[1]

Input field	Meaning and units	Accepted input
angularFrequency	Angular frequency in radians per matching time unit.	Required. Finite number.
delay	Delay	Required. Finite number; minimum 0.
convention	Convention	Required. Text; one of "exp-positive", "exp-negative"; maximum UTF-16 length 8192.

Output field	Interpretation	Returned shape
phaseShift	Phase Shift	Required. Finite number.

json

{
  "input": {
    "angularFrequency": 2,
    "delay": 0.5,
    "convention": "exp-positive"
  },
  "output": {
    "phaseShift": -1
  }
}

Limitations and assumptions

Angular frequency and time units must match; phase is not wrapped or measured from data.
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

Calculation and input contract: cybernetics/sample-hold-delay-phase-sign — tool.io

Similar or alternative tools

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