Description
Fold an integer mode into a signed sampled frequency.
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.
Fold an integer mode into a signed sampled frequency.
When to use this tool
Use Discrete Mode Frequency Fold when checking the stated grid-coordinate, periodic-image or sampled-mode convention.
How to use the tool and how it works
- Enter modeIndex, sampleCount, sampleRate, positiveNyquist. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read foldedIndex, frequency, nyquistTie. Inspect nyquistTie before interpreting the associated values.
Fold an integer mode into a signed sampled frequency. Require positive whole sampleCount and sampleRate > 0; reduce modeIndex using exact integer modulo, apply the supplied Nyquist sign and return frequency = foldedIndex*sampleRate/N.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| modeIndex | Mode Index | Required. Safe integer. |
| sampleCount | Sample Count | Required. Safe integer; minimum 1. |
| sampleRate | Sample Rate | Required. Finite number; strictly above 0. |
| positiveNyquist | Positive Nyquist | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| foldedIndex | Folded Index | Required. Safe integer. |
| frequency | Frequency | Required. Finite number. |
| nyquistTie | Even sample count with reduced index exactly N/2; sign is selected by positiveNyquist. | Required. Boolean. |
{
"input": {
"modeIndex": 7,
"sampleCount": 8,
"sampleRate": 80,
"positiveNyquist": true
},
"output": {
"foldedIndex": -1,
"frequency": -10,
"nyquistTie": false
}
}Limitations and assumptions
- Frequency inherits sample-rate units; negative modes and exact Nyquist ties are conventions, not inferred signal content.
- 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
- Spectral Derivative One Mode Factor
Return one Fourier derivative factor under an explicit complex convention.
- Computational Physics: Spectral Mode Nyquist Sign
Map a Fourier index to a signed mode.