Enter Signal Data
Use one main page column. The form fields below shift into 3, 2, or 1 columns by screen size.
Example Data Table
This sample shows a short vibration signal prepared for dyadic decomposition.
| Sample Index | Amplitude | Observation |
|---|---|---|
| 1 | 0.25 | Startup motion |
| 2 | 0.62 | Speed rising |
| 3 | 1.10 | Transient peak |
| 4 | 0.76 | Settling begins |
| 5 | 0.18 | Mid-band response |
| 6 | -0.30 | Phase swing |
| 7 | -0.92 | Negative excursion |
| 8 | -1.26 | Fault-like impulse zone |
Formula Used
Discrete wavelet decomposition:
aj[k] = Σ h[m] · aj-1[2k + m]
dj[k] = Σ g[m] · aj-1[2k + m]
E = Σ x[n]2
RMS = √((Σ x[n]2) / N)
σ̂ = median(|d1|) / 0.6745
λ = σ̂ √(2 ln N) × threshold factor
What each term means:
- aj[k] is the approximation coefficient at level j.
- dj[k] is the detail coefficient at level j.
- h[m] is the low-pass analysis filter.
- g[m] is the high-pass analysis filter.
- λ is the suggested denoising threshold after scaling.
How to Use This Calculator
- Enter the signal name and paste numeric samples into the signal box.
- Set the sampling frequency so the tool can estimate frequency bands.
- Select a wavelet family that matches the sharpness or smoothness you need.
- Choose decomposition levels, boundary extension, and normalization method.
- Decide whether to remove the mean before decomposition.
- Set the threshold factor to scale the universal noise threshold.
- Click Run Wavelet Transform to show the result below the header.
- Review coefficient energy, entropy, RMS, and threshold retention by level.
- Export the output using the CSV or PDF buttons.
FAQs
1. What does this tool calculate?
It performs multi-level discrete wavelet decomposition on a sampled signal. It reports approximation and detail coefficients, energy, entropy, RMS, detail bands, and a threshold suggestion for denoising review.
2. When should I use Haar instead of Daubechies?
Use Haar for abrupt changes, simple step-like behavior, and quick interpretation. Use Daubechies options when you want smoother filtering and better representation of gradual signal variation.
3. Why does the tool reduce my requested levels?
The maximum useful level depends on sample count. If the signal is too short, the tool automatically lowers the level count so the decomposition remains valid and interpretable.
4. What is the threshold value for?
The threshold is a denoising guide. Coefficients below it are often treated as weak or noise-dominated, while larger coefficients usually capture stronger transient or structural content.
5. Why are frequency bands only estimates?
Wavelet bands are dyadic approximations based on sampling rate and level. Real signals, filter length, and boundary handling can spread energy across nearby regions.
6. Should I remove the mean before analysis?
Yes, if you want to reduce DC bias and emphasize oscillatory behavior. Leave the mean intact when the baseline itself carries engineering meaning.
7. What does entropy tell me here?
Entropy shows how concentrated or dispersed coefficient energy is. Lower values suggest energy is focused in fewer coefficients, while higher values indicate more spread or complexity.
8. Can I use this for vibration and fault studies?
Yes. It is suitable for vibration screening, transient inspection, burst detection, bearing studies, and other engineering signals where time-localized frequency behavior matters.