Enter Signal and Analysis Options
The page stays single-column overall, while the calculator fields use a responsive 3-column, 2-column, and 1-column layout.
Example Data Table
This sample sequence approximates a cosine wave with a phase offset. You can load it directly into the calculator.
| Index n | Sample x[n] |
|---|---|
| 0 | 0.7071 |
| 1 | 0.0000 |
| 2 | -0.7071 |
| 3 | -1.0000 |
| 4 | -0.7071 |
| 5 | 0.0000 |
| 6 | 0.7071 |
| 7 | 1.0000 |
Formula Used
For each frequency bin k, the calculator evaluates the Discrete Fourier Transform:
X[k] = Σ x[n] · w[n] · e-j2πkn/N, for n = 0 to N-1
From the complex result:
Re{X[k]} = real part
Im{X[k]} = imaginary part
|X[k]| = √(Re² + Im²)
φ[k] = atan2(Im{X[k]}, Re{X[k]})
Wrapped phase stays inside the principal range. Unwrapped phase removes ±2π jumps between neighboring bins.
How to Use This Calculator
- Enter real-valued samples separated by commas, spaces, or line breaks.
- Set the sample spacing to match your acquisition interval.
- Choose a window to reduce leakage when the record is finite.
- Apply zero padding if you want denser frequency-bin spacing.
- Select wrapped, unwrapped, or both phase views for the graph.
- Use a magnitude threshold to hide unstable phase at weak bins.
- Press the calculate button and inspect the summary, chart, and table.
- Export the results as CSV or PDF when needed.
8 FAQs
1. What does the phase spectrum show?
It shows the angle of each Fourier coefficient. That angle describes how each sinusoidal component is shifted in time relative to a reference cosine at the same frequency.
2. Why do some bins show “Below threshold”?
Phase becomes unreliable when magnitude is extremely small. The threshold hides those unstable bins so weak numerical noise does not look like meaningful phase information.
3. What is wrapped phase?
Wrapped phase keeps every angle inside a principal interval, usually from -π to π or -180° to 180°. This makes values compact, but sudden jumps can appear.
4. What is unwrapped phase?
Unwrapped phase removes artificial ±2π discontinuities between adjacent bins. It is helpful when you want to inspect smooth trends or estimate delay from phase slope.
5. Does zero padding improve true frequency resolution?
Zero padding increases the number of displayed bins, so the graph looks smoother. It does not add new signal information, but it can help identify peak location more clearly.
6. Why use a window function?
Finite records can leak energy across bins. A window reduces leakage and often produces cleaner amplitude and phase estimates, especially when the signal period does not fit perfectly.
7. What sample spacing should I enter?
Enter the time interval between consecutive samples. For example, sampling at 1000 Hz means the spacing is 0.001 seconds per sample.
8. Can this calculator process complex input samples?
This version is designed for real-valued input sequences. If you need complex samples, the parser and form can be extended to accept separate real and imaginary series.