Signal Detrend Endpoint Gap Tool

Description

Audit an explicitly supplied linear detrend against two research signal endpoints.

Physiological models use measured signals, reference levels, rates, and physical balances. A content difference, normalized phase, or energy term depends on its unit system and model assumptions. Supplied coefficients and annotations define the calculation but do not establish biological plausibility or measurement accuracy.

Audit an explicitly supplied linear detrend against two research signal endpoints.

When to use this tool

Use Signal Detrend Endpoint Gap when you need this explicit signal, content, phase, flow, or physical-balance term under compatible supplied units.

How to use the tool and how it works

Enter firstValue, lastValue, suppliedSlope, elapsed. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read observedChange, predictedChange, residual. Use the output convention below.

For nonnegative elapsed return observedChange=lastValue-firstValue, predictedChange=suppliedSlope*elapsed, and residual=observedChange-predictedChange.^[1]

Input field	Meaning and units	Accepted input
firstValue	First Value	Required. Finite number.
lastValue	Last Value	Required. Finite number.
suppliedSlope	Supplied Slope	Required. Finite number.
elapsed	Elapsed	Required. Finite number; minimum 0.

Output field	Interpretation	Returned shape
observedChange	Observed Change	Required. Finite number.
predictedChange	Predicted Change	Required. Finite number.
residual	Signed observed-minus-implied discrepancy under the stated formula.	Required. Finite number.

json

{
  "input": {
    "firstValue": 2,
    "lastValue": 10,
    "suppliedSlope": 1,
    "elapsed": 6
  },
  "output": {
    "observedChange": 8,
    "predictedChange": 6,
    "residual": 2
  }
}

Limitations and assumptions

Signal values need one unit and slope must be signal units per elapsed-time unit. Only endpoint change is assessed; the intermediate waveform is not detrended or inspected.
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. Signed zero is exported as zero.

Alternative or Complementary methods

Choose a physiological and measurement model suited to the signal or experiment. Verify coefficients, unit conversions, baseline definitions, and sampling support before combining local terms.

References

Calculation and input contract: physiology/signal-detrend-endpoint-gap — tool.io

Similar or alternative tools

Research Signal Baseline Shift
Compare supplied research signal baseline choices without physiological diagnosis.
Signal Reference Phase Gap
For positive period and radiansPerPeriod wrap signalPhase-referencePhase to the shortest signed phaseGap, subtracting one period when the wrapped gap exceeds half a period; return angularGap=phaseGap/period*radiansPerPeriod.