Harmonic Analysis Calculator Form
Use the responsive three-column layout on large screens, two columns on medium screens, and one column on mobile screens.
Example Data Table
This example uses eight equally spaced samples from a waveform containing a fundamental term and a third harmonic term.
| Index | Angle (deg) | Sample Value |
|---|---|---|
| 0 | 0 | 0.000 |
| 1 | 45 | 4.596 |
| 2 | 90 | 3.500 |
| 3 | 135 | 4.596 |
| 4 | 180 | 0.000 |
| 5 | 225 | -4.596 |
| 6 | 270 | -3.500 |
| 7 | 315 | -4.596 |
Formula Used
The calculator assumes your values are equally spaced across one full period. It estimates the trigonometric Fourier series of the sampled waveform.
x(θ) ≈ a₀/2 + Σ [aₙ cos(nθ) + bₙ sin(nθ)]
a₀ = (2/N) Σ x[k]
aₙ = (2/N) Σ x[k] cos(2πnk/N)
bₙ = (2/N) Σ x[k] sin(2πnk/N)
Amplitude Cₙ = √(aₙ² + bₙ²)
Phase φₙ = atan2(bₙ, aₙ)
THD = √(Σ Cₙ², n≥2) / C₁ × 100%
RMS = √[(a₀/2)² + 0.5 Σ(aₙ² + bₙ²)]
These equations work well when one full cycle is sampled uniformly. Uneven spacing or incomplete periods can distort the estimated spectrum.
How to Use This Calculator
- Enter a signal name and the measurement unit.
- Type the fundamental frequency of the waveform in hertz.
- Choose how many harmonics should be evaluated.
- Paste equally spaced sample values covering one complete period.
- Click Analyze Harmonics to generate coefficients, amplitudes, phases, RMS, THD, and graphs.
- Review the waveform reconstruction and spectrum chart.
- Export the computed results using the CSV or PDF buttons.
- Use the example dataset first if you want to test the page quickly.
FAQs
1. What does this calculator analyze?
It analyzes periodic sample data using Fourier-style harmonic decomposition. You get DC content, harmonic coefficients, amplitudes, phase angles, RMS value, and total harmonic distortion from one complete sampled cycle.
2. Do my samples need equal spacing?
Yes. The method assumes uniform spacing over one full period. If the spacing changes or the period is incomplete, the coefficients and reconstructed waveform can become misleading.
3. What is the meaning of an and bn?
The an terms measure cosine content, while the bn terms measure sine content. Together they describe the strength and angular position of each harmonic component.
4. What does the amplitude column show?
It shows the magnitude of each harmonic component, computed from the coefficient pair. A larger amplitude means that harmonic contributes more strongly to the original waveform shape.
5. How is THD interpreted?
THD compares all higher harmonic amplitudes to the fundamental amplitude. A smaller percentage indicates a cleaner waveform, while a larger percentage indicates stronger distortion from higher-order harmonics.
6. Why does phase matter?
Phase shows where each harmonic is shifted within the cycle. Two waveforms can have similar amplitudes but look different when their harmonic phases are different.
7. Can I use many more samples?
Yes. More samples usually improve resolution, especially for sharper waveforms. Very large inputs still work, but they increase processing time and make tables and charts denser.
8. When should I use the example data?
Use it when you want to verify layout, exports, charts, and result logic before entering your own dataset. It is also useful for learning how harmonic content affects waveform reconstruction.