Subthreshold Oscillation Frequency

Estimate subthreshold oscillation frequency from interpolated upward reference crossings; spikes and drift must be removed beforehand and cadence must resolve the waveform.

Description

Repeated upward crossings of a reference voltage provide an oscillation-period estimate.

Repeated upward crossings of a reference voltage provide an oscillation-period estimate. Crossing times can be more precise than raw sample times through interpolation.

The tool returns upcrossingTimesSeconds (upcrossing times seconds); estimatedFrequencyHz (estimated 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 Subthreshold Oscillation Frequency

Use Subthreshold Oscillation Frequency when you already have timesSeconds, voltagesMv, referenceMv and want upcrossingTimesSeconds, estimatedFrequencyHz. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Subthreshold Oscillation Frequency and understand its results

Enter timesSeconds, voltagesMv, referenceMv 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 upcrossingTimesSeconds, estimatedFrequencyHz. 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
timesSeconds	Times seconds	list of number	Required
voltagesMv	Voltages mv	list of number	Required
referenceMv	Reference mv	number	Required

Detect transitions from strictly below to at least the reference, linearly interpolate their times, and require at least two upward crossings.

frequency = (crossingCount−1)/(lastCrossing−firstCrossing)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "timesSeconds": [
      0,
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "voltagesMv": [
      -1,
      1,
      -1,
      1,
      -1,
      1,
      -1
    ],
    "referenceMv": 0
  },
  "output": {
    "upcrossingTimesSeconds": [
      0.5,
      2.5,
      4.5
    ],
    "estimatedFrequencyHz": 0.5
  }
}

Limitations and assumptions

This is a crossing-based frequency, not a spectral fit. Noise, threshold choice and irregular oscillations can alter the result.

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

Impedance Amplitude: Fit sine/cosine components with a DC intercept to simultaneous voltage/current samples at a supplied injection frequency and derive complex impedance magnitude/phase; no FFT leakage assumption is needed. Resonance Frequency: Find the unique sampled impedance maximum and distinguish an interior resonance candidate from an edge maximum; ratio references the lowest measured frequency, not extrapolated DC.

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

Impedance Amplitude
Fit sine/cosine components with a DC intercept to simultaneous voltage/current samples at a supplied injection frequency and derive complex impedance magnitude/phase; no FFT leakage assumption is needed.
Resonance Frequency
Find the unique sampled impedance maximum and distinguish an interior resonance candidate from an edge maximum; ratio references the lowest measured frequency, not extrapolated DC.