Calculator Input
Example Data Table
| # | x | y |
|---|---|---|
| 1 | 0.000 | 0.000000 |
| 2 | 0.125 | 1.207107 |
| 3 | 0.250 | 1.000000 |
| 4 | 0.375 | 0.207107 |
| 5 | 0.500 | 0.000000 |
| 6 | 0.625 | -0.207107 |
| 7 | 0.750 | -1.000000 |
| 8 | 0.875 | -1.207107 |
Formula Used
Numerical Fourier transform:
F(fk) ≈ Σ [ wn · yn · e-i 2π fk xn ]
Real part: Re(F) = Σ [ wn · yn · cos(2π fk xn) ]
Imaginary part: Im(F) = -Σ [ wn · yn · sin(2π fk xn) ]
Magnitude: |F| = √(Re² + Im²)
Phase: φ = atan2(Im, Re)
Trapezoidal weights are used for numerical integration. For irregular spacing, the calculator estimates each sample weight from neighboring x values. Optional detrending removes mean or linear drift before the window is applied. Windowing reduces leakage and helps isolate nearby harmonics more cleanly.
How to Use This Calculator
- Choose x,y pairs if every sample has its own x coordinate.
- Choose y values only when samples are evenly spaced and enter the spacing.
- Paste your values into the data area. One pair per line works best.
- Set the frequency start, end, and number of bins for the sweep.
- Pick a detrend method and window function based on your signal quality.
- Choose a normalization style that matches your reporting preference.
- Submit the form to generate the transform summary, graphs, and table.
- Use the download buttons to save the numerical spectrum as CSV or PDF.
FAQs
1) What does this calculator actually compute?
It numerically estimates the Fourier transform of your sampled data over a frequency range you choose. It returns real, imaginary, magnitude, phase, and power values for every tested frequency bin.
2) Can I use irregularly spaced x values?
Yes. In pair mode, the calculator sorts x values and applies trapezoidal integration weights. That makes it suitable for many irregularly sampled datasets where direct FFT assumptions do not hold.
3) Why should I remove the mean first?
Removing the mean reduces the zero-frequency component. That often prevents the DC term from dominating the spectrum and makes periodic features easier to identify, especially when the signal rides on a fixed offset.
4) What is the difference between window choices?
Rectangular keeps the signal unchanged. Hann, Hamming, and Blackman taper the ends and reduce leakage. Stronger tapering usually lowers sidelobes but also broadens peaks slightly.
5) When should I ignore the DC peak?
Ignore the DC peak when you want the strongest oscillatory frequency rather than the overall offset. This is useful for vibration, audio, and sensor signals with a nonzero baseline.
6) How many frequency bins should I use?
Use more bins when you want a finer sweep across the chosen range. Higher bin counts improve visual detail, but they also increase computation time and enlarge exported tables.
7) What normalization should I choose?
Choose weight normalization for integration-style amplitudes, point normalization for average-style scaling, and square-root normalization for balanced magnitude comparisons. Use none when you want raw numerical sums.
8) Is this the same as a standard FFT?
Not exactly. A standard FFT assumes uniform spacing and specific sample counts. This calculator performs a direct numerical transform, which is slower but more flexible for irregular or custom frequency grids.