Calculator inputs
Example data table
These sample points come from the default mixed waveform included in the calculator.
| Index | Time (s) | Amplitude |
|---|---|---|
| 0 | 0.0000 | 0.590553 |
| 1 | 0.0156 | 1.380442 |
| 2 | 0.0313 | 1.365448 |
| 3 | 0.0469 | 0.983259 |
| 4 | 0.0625 | 0.882000 |
| 5 | 0.0781 | 1.074475 |
| 6 | 0.0938 | 0.943566 |
| 7 | 0.1094 | 0.087312 |
Formula used
Discrete Fourier transform: X[k] = Σ x[n] · e-j2πkn/N
Resolved frequency: fk = k · fs / N
Amplitude estimate: Ak = 2|X[k]| / (N · coherent gain), except DC and Nyquist bins
Spectral centroid: Σ(fk · Ak) / ΣAk
Total harmonic distortion: THD = √(A22 + A32 + …) / A1 × 100%
The calculator performs a discrete spectrum evaluation on sampled data, applies the selected window, optionally removes DC offset, and then resolves dominant bins, harmonics, and signal quality indicators.
How to use this calculator
- Paste evenly spaced sample values into the input box.
- Enter the sample rate used during acquisition.
- Add an expected fundamental when harmonic distortion matters.
- Add a target frequency when you want a specific component check.
- Choose a window to reduce leakage for incomplete cycles.
- Set the peak threshold and number of leading components.
- Submit the form to display results above the calculator.
- Use the CSV and PDF buttons to export the spectral report.
Frequently asked questions
1. What does this calculator measure?
It converts time-domain samples into a frequency-domain view. You can inspect dominant frequencies, amplitudes, phases, harmonic behavior, RMS, energy, and spectral centroid from one submission.
2. Why is sample rate important?
Sample rate determines the Nyquist limit and frequency spacing. A low rate can hide fast content, while a higher rate improves available frequency range.
3. When should I remove DC?
Remove DC when you want the average value separated from oscillatory content. Keeping DC is useful when offset itself is a meaningful part of the signal.
4. What does the window choice change?
Windowing reduces leakage when a captured waveform does not align perfectly with an integer number of cycles. Hann and Hamming are common general-purpose choices.
5. Why does the resolved frequency differ from my expected value?
The spectrum resolves to fixed bins spaced by sample rate divided by sample count. Your expected value is matched to the nearest available bin.
6. What is total harmonic distortion here?
THD compares the combined amplitude of higher harmonics with the first harmonic amplitude. It helps judge waveform purity and distortion severity.
7. Can I use non-sinusoidal sample sets?
Yes. Any evenly sampled numeric waveform can be analyzed. Complex waveforms usually show multiple peaks and stronger harmonic content than pure sine waves.
8. Why is there a 512-sample limit?
This page performs spectrum calculations on the server without a specialized fast transform library. The limit keeps response time practical and stable.