THz Waveform Spectrum

Compute a direct discrete magnitude spectrum from a THz time-domain waveform.

Description

A direct discrete Fourier transform converts uniformly spaced THz field samples into magnitude bins.

A direct discrete Fourier transform converts uniformly spaced THz field samples into magnitude bins. The implementation returns the full unnormalized spectrum.^[1]

Compute a direct discrete magnitude spectrum from a THz time-domain waveform.

When to use THz Waveform Spectrum

Use this tool to compute a direct discrete magnitude spectrum from a THz time-domain waveform.

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.

How to use THz Waveform Spectrum and understand its results

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
Enter fieldSamples, sampleIntervalPicoseconds using the field table and calculation rules, then run the tool.
Read frequenciesTerahertz, magnitudeSpectrum. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
fieldSamples	Time-domain field samples	list of number	Required
sampleIntervalPicoseconds	Sample interval (ps)	number; minimum: 0	Required

Enter nonempty finite samples and positive spacing in ps. Return n frequencies in THz and n magnitudes in DFT order, including DC and the wrapped negative-frequency half.

magnitude_k=|Σ_j field_j exp(−2πijk/n)|; frequency_k=k/(nΔt_ps)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
frequenciesTerahertz	DFT frequencies (THz)	list of number
magnitudeSpectrum	DFT magnitudes	list of number

json

{
  "input": {
    "fieldSamples": [
      1,
      0,
      -1,
      0
    ],
    "sampleIntervalPicoseconds": 1
  },
  "output": {
    "frequenciesTerahertz": [
      0,
      0.25,
      0.5,
      0.75
    ],
    "magnitudeSpectrum": [
      0,
      2,
      2.4492935982947064e-16,
      2
    ]
  }
}

Limitations and assumptions

No window, baseline removal or amplitude normalization is applied. Runtime scales quadratically with sample count; use short scoped traces.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use THz Complex Conductivity: Convert complex relative permittivity to complex conductivity under an exp(-iωt) convention. For a complementary task, use THz Time-of-Flight Depth: Convert a THz reflection delay into subsurface layer depth.

References

THz Waveform Spectrum — tool.io

Similar or alternative tools

THz Complex Conductivity
Convert complex relative permittivity to complex conductivity under an exp(-iωt) convention.
THz Time-of-Flight Depth
Convert a THz reflection delay into subsurface layer depth.