FFT Real Frequency Bin Weight

Description

Choose a supplied real-FFT bin's one-sided power weight.

Numerical physics calculations depend on discretization, index conventions, boundary conditions and model units. A local force kick is only part of an integration method, a stencil residual is not a solved field, and a one-sided power weight is not a spectral-density normalization. Floating-point resolution also limits grid and coordinate representations.

Choose a supplied real-FFT bin's one-sided power weight.

When to use this tool

Use FFT Real Frequency Bin Weight when you already have sampleCount, binIndex and need to choose a supplied real-FFT bin's one-sided power weight.

How to use the tool and how it works

Enter sampleCount, binIndex. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read oneSidedPowerWeight. Use the output convention below.

Require positive safe sampleCount and whole binIndex in [0,floor(N/2)]; weight=1 at DC or the even-N Nyquist bin, otherwise 2.^[1]

One-sided real-data power combines the contributions of paired positive and negative frequencies. Choosing power versus power-density normalization remains a separate step from this bin weight.^[2]

Input field	Meaning and units	Accepted input
sampleCount	Sample Count	Required. Safe integer; minimum 1.
binIndex	Bin Index	Required. Safe integer; minimum 0.

Output field	Interpretation	Returned shape
oneSidedPowerWeight	One for DC and an even-length Nyquist bin, two for all other valid one-sided bins; a power weight, not an amplitude multiplier.	Required. Safe integer.

json

{
  "input": {
    "sampleCount": 8,
    "binIndex": 2
  },
  "output": {
    "oneSidedPowerWeight": 2
  }
}

Limitations and assumptions

This weight is for folding symmetric power, not doubling Fourier amplitudes or normalizing a PSD. No transform, sampling rate, window or spectrum is computed.
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 discretized model, integration algorithm and boundary treatment. Assess convergence, conservation and stability with the full calculation; individual residuals, CFL components, relaxation terms and index mappings do not establish numerical accuracy or physical validity.

References

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