Spectral Edge Frequency
Locate a requested integrated PSD fraction by trapezoidal integration and within-bin linear-density inversion; not a percentile of frequency samples.
Description
Spectral edge frequency locates the frequency below which a chosen fraction of integrated power lies.
Spectral edge frequency locates the frequency below which a chosen fraction of integrated power lies. It requires treating power density as a function of frequency.
The tool returns edgeFrequencyHz (edge frequency hz). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Spectral Edge Frequency
Use Spectral Edge Frequency when you already have frequenciesHz, powerDensity, powerFraction and want edgeFrequencyHz. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Spectral Edge Frequency and understand its results
- Enter frequenciesHz, powerDensity, powerFraction using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read edgeFrequencyHz. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| frequenciesHz | Frequencies hz | list of number | Required |
| powerDensity | Power density | list of number | Required |
| powerFraction | Power fraction | number | Required |
Use increasing nonnegative frequencies and nonnegative aligned densities. Trapezoidally integrate, then solve within the selected linear-density segment by bisection.
∫fmin^edge PSD(f)df = powerFraction × ∫fmin^fmax PSD(f)df The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"frequenciesHz": [
0,
10,
20
],
"powerDensity": [
1,
1,
1
],
"powerFraction": 0.75
},
"output": {
"edgeFrequencyHz": 15
}
}Limitations and assumptions
The input is already an estimated spectrum; no FFT, artifact rejection or sampling correction occurs. Zero total power is rejected.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
EEG Asymmetry Index: Compute epoch-paired ln(right power)−ln(left power) and its average; electrodes, band selection, referencing and artifact rejection are caller responsibilities. Contrast Sensitivity: Build a contrast-sensitivity function and trapezoidal area in log10 frequency/log10 sensitivity space from measured Michelson thresholds.
Methodological background: Digital Library of Mathematical Functions: Quadrature.1
References
-
Digital Library of Mathematical Functions: Quadrature — National Institute of Standards and Technology
Similar or alternative tools
- EEG Asymmetry Index
Compute epoch-paired ln(right power)−ln(left power) and its average; electrodes, band selection, referencing and artifact rejection are caller responsibilities.
- Contrast Sensitivity
Build a contrast-sensitivity function and trapezoidal area in log10 frequency/log10 sensitivity space from measured Michelson thresholds.