Description
Return one Fourier derivative factor under an explicit complex convention.
Numerical grids and sampled modes require explicit coordinate, boundary and sign conventions. A staggered location, minimum-image gap or Nyquist label is one component of a discretization rather than a complete field solve or unique physical interpretation.
Return one Fourier derivative factor under an explicit complex convention.
When to use this tool
Use Spectral Derivative One Mode Factor when checking the stated grid-coordinate, periodic-image or sampled-mode convention.
How to use the tool and how it works
- Enter real, imaginary, wavenumber. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivativeReal, derivativeImaginary. Use the output convention below.
Return one Fourier derivative factor under an explicit complex convention. derivativeReal = -wavenumber*imaginary, derivativeImaginary = wavenumber*real, implementing multiplication by i*k.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| real | Real | Required. Finite number. |
| imaginary | Imaginary | Required. Finite number. |
| wavenumber | Angular wavenumber in radians per matching length, under derivative multiplication by i*k. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivativeReal | Derivative Real | Required. Finite number. |
| derivativeImaginary | Derivative Imaginary | Required. Finite number. |
{
"input": {
"real": 2,
"imaginary": 3,
"wavenumber": 4
},
"output": {
"derivativeReal": -12,
"derivativeImaginary": 8
}
}Limitations and assumptions
- Wavenumber is radians per matching length; transform sign, Nyquist policy and complete differentiation are not selected.
- 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
Use the complete mesh, transform convention and boundary conditions for a consistent numerical simulation or physical interpretation.
References
Similar or alternative tools
- Computational Physics: Spectral Mode Nyquist Sign
Map a Fourier index to a signed mode.
- Discrete Mode Frequency Fold
Fold an integer mode into a signed sampled frequency.