Examples
Examples
Try the starting example
- Real sample components
- 1,0,0,0
- Imaginary sample components
- 0,0,0,0
- Direction: forward or inverse
- forward
- Normalization: backward, forward or ortho
- backward
- Real transform components
- 1, 1, 1, 1
- Imaginary transform components
- 0, 0, 0, 0
- Two-sided bin magnitudes
- 1, 1, 1, 1
- Bin phases (degrees; zero at numerical zero magnitude)
- 0, 0, 0, 0
Try another scenario
- Real sample components
- 1,1,1,1
- Imaginary sample components
- 0,0,0,0
- Direction: forward or inverse
- forward
- Normalization: backward, forward or ortho
- backward
- Real transform components
- 4, 0, 0, 0
- Imaginary transform components
- 0, 0, 0, 0
- Two-sided bin magnitudes
- 4, 0, 0, 0
- Bin phases (degrees; zero at numerical zero magnitude)
- 0, 0, 0, 0
Calculation method
Calculation method
Real transform components
Sum samples against exp(−2πikj/N) for forward or exp(+2πikj/N) for inverse, retaining the real components.
Imaginary transform components
Imaginary components of the same transform.
Two-sided bin magnitudes
sqrt(real²+imag²) per bin; this is not a one-sided amplitude spectrum.
Bin phases (degrees; zero at numerical zero magnitude)
atan2(imaginary,real) in degrees; roundoff-scale components are set to zero before phase evaluation. Backward scales inverse by 1/N, forward scales forward by 1/N, ortho scales both by 1/sqrt(N).
Symbols and units
- a
- Real sample components
- b
- Imaginary sample components
- c
- Direction: forward or inverse
- d
- Normalization: backward, forward or ortho
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Direct O(N²) real/complex DFT for at most 128 matched samples. No sample rate, windowing, frequency labels or one-sided power correction is inferred. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
NumPy: DFT normalization and transform conventions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.