Calculator Inputs
Example Data Table
| Sample Index | Signal Value | Meaning |
|---|---|---|
| 0 | 1 | Starting amplitude |
| 1 | 0 | Zero crossing region |
| 2 | -1 | Negative swing |
| 3 | 0 | Return toward center |
| 4 | 1 | Repeated positive cycle |
| 5 | 0 | Midpoint sample |
| 6 | -1 | Repeated negative cycle |
| 7 | 0 | Cycle completion |
Example input string: 1, 0, -1, 0, 1, 0, -1, 0 with sampling rate 8 Hz.
Formula Used
The calculator evaluates the Discrete Fourier Transform for each frequency bin and then takes the absolute value of the complex result.
DFT: X(k) = Σ x(n) · e-j2πkn/N, for n = 0 to N - 1
Magnitude Spectrum: |X(k)| = √(Re(X(k))2 + Im(X(k))2)
Bin Frequency: f(k) = k · fs / N
Amplitude-Style Normalization: |X(k)| = 2|X(k)| / N for interior single-sided bins.
Windowing reduces leakage, while zero padding improves bin spacing display without adding new signal information.
How to Use This Calculator
- Paste or type signal samples as comma-separated values.
- Enter the sampling rate in hertz.
- Select a window function for leakage control.
- Choose whether to apply zero padding.
- Pick a normalization style that matches your workflow.
- Select single-sided or double-sided spectrum output.
- Press the calculate button to place results above the form.
- Review the peak frequency, data table, chart, and exports.
Frequently Asked Questions
1. What does the magnitude spectrum show?
It shows how strongly each frequency component appears in your sampled signal. Larger magnitudes indicate stronger contributions from specific frequencies or periodic patterns.
2. Why is the sampling rate required?
The sampling rate converts spectral bins into real frequencies measured in hertz. Without it, you only know the bin positions, not the physical frequency scale.
3. What is the difference between single-sided and double-sided spectra?
A single-sided spectrum keeps nonnegative frequencies for real signals. A double-sided spectrum includes the full transform range and is useful for broader complex-frequency inspection.
4. Why use Hann or Hamming windows?
These windows reduce spectral leakage when your signal does not complete an exact integer number of cycles inside the observation frame. They trade some peak sharpness for cleaner sidelobes.
5. Does zero padding improve accuracy?
Zero padding does not create new information. It refines displayed bin spacing and makes the spectrum plot smoother, which can help estimate peak locations visually.
6. What does amplitude normalization do?
Amplitude-style normalization rescales the spectrum so peak values better resemble signal amplitude conventions for a single-sided plot. It is practical for comparison and reporting.
7. Can I analyze non-sinusoidal signals?
Yes. Any sampled waveform can be transformed. Complex shapes usually produce multiple harmonics and broader spectral content, which this calculator can list and visualize.
8. Why might the strongest peak seem unexpected?
Unexpected peaks can come from leakage, coarse sample counts, poor normalization choices, or a sampling rate mismatch. Try changing windowing, padding, or verifying the input sequence.