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Spectral Energy Bin Width Reference

Integrate an explicitly uniform energy density over a supplied frequency-bin width without changing spectral coordinate systems.

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Description

Calculate one energy-density bin contribution using a supplied width.

A unit conversion preserves the underlying quantity only when the source and target definitions match. Ratios such as strain and relative density are dimensionless, whereas spectral densities need a bandwidth and radiance needs projected angular coverage. A supplied label or scale factor does not verify the physical definition or measurement conditions.

Calculate one energy-density bin contribution using a supplied width.

When to use this tool

Use Spectral Energy Bin Width Reference when you already have energyDensityPerHertz, binWidthHertz and need to calculate one energy-density bin contribution using a supplied width.

How to use the tool and how it works

  1. Enter energyDensityPerHertz, binWidthHertz. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read binEnergy. Use the output convention below.

Require energyDensityPerHertz and binWidthHertz>=0; multiply to return binEnergy.1

Input fieldMeaning and unitsAccepted input
energyDensityPerHertzEnergy/Hz, assumed constant or already averaged within the supplied bin.Required. Finite number; minimum 0.
binWidthHertzBin Width HertzRequired. Finite number; minimum 0.
Output fieldInterpretationReturned shape
binEnergyenergyDensityPerHertz*binWidthHertz; not an integration of a varying spectrum.Required. Finite number.
json
{
  "input": {
    "energyDensityPerHertz": 2.5,
    "binWidthHertz": 4
  },
  "output": {
    "binEnergy": 10
  }
}

Limitations and assumptions

  • Density must represent the bin-average or an assumed constant over the bin. No spectrum is integrated, sampling convention chosen or actual energy measured.
  • 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

Check the original quantity definition, calibration and unit basis before converting. Integrate a varying spectrum or angular distribution when a constant-bin or uniform-radiance approximation is insufficient, and retain the relevant reference conditions.

References

  1. Calculation and input contract: convert/spectral-energy-bin-width-reference — tool.io

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