Sample Delay Phase Reference Gap Tool

Description

Compare sample-delay phase with a reference.

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.

Compare sample-delay phase with a reference.

When to use this tool

Use Sample Delay Phase Reference Gap when checking one supplied sample, delay or quantization convention.

How to use the tool and how it works

Enter angularFrequency, delaySamples, samplePeriod, referencePhase. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read phaseLag, signedGap. Use the output convention below.

Compare sample-delay phase with a reference. Require nonnegative whole delaySamples and positive samplePeriod; phaseLag = -angularFrequency*delaySamples*period, signedGap subtracts referencePhase.^[1]

Input field	Meaning and units	Accepted input
angularFrequency	Angular frequency in radians per matching time unit.	Required. Finite number.
delaySamples	Delay Samples	Required. Safe integer; minimum 0.
samplePeriod	Sample Period	Required. Finite number; strictly above 0.
referencePhase	Reference Phase	Required. Finite number.

Output field	Interpretation	Returned shape
phaseLag	Phase Lag	Required. Finite number.
signedGap	Signed Gap	Required. Finite number.

json

{
  "input": {
    "angularFrequency": 2,
    "delaySamples": 3,
    "samplePeriod": 0.5,
    "referencePhase": -2
  },
  "output": {
    "phaseLag": -3,
    "signedGap": -1
  }
}

Limitations and assumptions

Use radians and a compatible time basis; no frequency response or loop stability is inferred.
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-delay-phase-reference-gap — tool.io

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