Calculator Inputs
Example Data Table
This example uses a mixed periodic waveform sampled every 0.125 seconds.
| Index | Time (s) | Sample Value | Squared Value |
|---|---|---|---|
| 0 | 0.0000 | 0.0000 | 0.0000 |
| 1 | 0.1250 | 0.7362 | 0.5420 |
| 2 | 0.2500 | 1.2071 | 1.4571 |
| 3 | 0.3750 | 1.2774 | 1.6318 |
| 4 | 0.5000 | 1.0000 | 1.0000 |
| 5 | 0.6250 | 0.5703 | 0.3252 |
| 6 | 0.7500 | 0.2071 | 0.0429 |
| 7 | 0.8750 | 0.0291 | 0.0008 |
Formula Used
\( y[n] = (x[n] - \mu)\,w[n] \)
Here, \(x[n]\) is the input sample, \(\mu\) is the mean if detrending is enabled, and \(w[n]\) is the chosen window.
\( E_t = \Delta t \sum_{n=0}^{N-1} |y[n]|^2 \)
This approximates the continuous signal energy from evenly spaced samples.
\( Y[k] = \sum_{n=0}^{M-1} y[n] e^{-j2\pi kn/M} \)
Here, \(M\) is the FFT length after optional zero padding.
\( E_f = \frac{\Delta t}{M}\sum_{k=0}^{M-1}|Y[k]|^2 \)
For a correctly computed transform, \(E_t\) and \(E_f\) should closely match.
Band energy is the sum of one-sided bin energies between the chosen minimum and maximum frequencies.
Band percentage = \( \frac{E_{band}}{E_t}\times100 \)
How to Use This Calculator
- Enter a signal name if you want labeled reports.
- Set the sampling interval to match your measured data spacing.
- Paste the sample values into the textarea.
- Select a window if you want reduced spectral leakage.
- Enable mean removal when DC offset should be excluded.
- Choose FFT points equal to or larger than your sample count.
- Set the frequency band for focused energy measurement.
- Press the calculate button to display results above the form.
- Review the cards, tables, and graphs.
- Download CSV or PDF reports when needed.
FAQs
1. What does Fourier energy mean?
Fourier energy measures how total signal energy appears across frequency bins. It lets you compare time-domain energy with spectral energy using Parseval’s theorem.
2. Why can time and frequency energy differ slightly?
Small differences usually come from floating-point rounding, windowing choices, or coarse sample spacing. A tiny mismatch is normal in numerical calculations.
3. When should I remove the mean?
Remove the mean when your data contains a DC offset and you want to focus on oscillatory content. Keep it when the offset itself is meaningful.
4. What does zero padding change?
Zero padding improves frequency-bin spacing and makes the spectrum look smoother. It does not add new signal information or change total energy.
5. Why use a window function?
A window reduces leakage when sampled data does not contain an exact integer number of cycles. Different windows trade resolution for leakage control.
6. What is band energy useful for?
Band energy helps isolate vibration ranges, filter zones, communication channels, or harmonic groups. It shows how much energy lives inside a selected interval.
7. Is this calculator for discrete or continuous signals?
It works from discrete samples and approximates continuous energy using the sampling interval. Better sampling quality gives better energy estimates.
8. How many samples should I enter?
Use enough samples to represent the waveform clearly, but keep the dataset practical for server-side processing. This version works best at 512 samples or fewer.