Analyze convoluted measurements using stable regularized inverse filtering. View reconstructed signals, residuals, and fit quality. Download reports and visualize frequency-sensitive recovery across sampled datasets.
| Sample | Measured response | Impulse response | Reference source |
|---|---|---|---|
| 0 | 0.2000 | 0.2000 | 1.0000 |
| 1 | 1.2000 | 0.6000 | 3.0000 |
| 2 | 3.0000 | 0.2000 | 5.0000 |
| 3 | 4.4000 | — | 4.0000 |
| 4 | 3.8000 | — | 2.0000 |
| 5 | 2.0000 | — | — |
| 6 | 0.4000 | — | — |
This example shows a short source sequence blurred by a three-tap impulse response. The calculator attempts to recover the original source from the measured response.
Regularized frequency-domain deconvolution: X(k) = Y(k) × H*(k) / (|H(k)|² + λ)
Inverse transform: x[n] = IDFT{X(k)}
Reconvolution check: ŷ[n] = x[n] * h[n]
Residual: r[n] = y[n] - ŷ[n]
Here, Y(k) is the measured spectrum, H(k) is the impulse response spectrum, H*(k) is its complex conjugate, and λ limits noise amplification when spectral bins become very small.
It estimates an original input sequence from a measured output and a known impulse response. This is useful in controls, instrumentation, imaging, vibration analysis, and signal restoration tasks.
Pure inverse filtering can explode when the kernel spectrum contains tiny values. Regularization adds stability, reduces noise amplification, and usually produces more realistic recovered signals.
Start with a very small value, then increase it gradually until the recovered signal stops oscillating excessively. Noisy measurements usually require a larger value than clean laboratory data.
For short finite signals, a common estimate is observed length minus kernel length plus one. Longer lengths can expose padding effects instead of meaningful recovered content.
Negative values can appear when the best mathematical fit requires them, especially with oscillatory kernels, measurement noise, or imperfect impulse responses. They are not always errors.
Normalize when the kernel should preserve total gain and its sample sum represents the system scale. Leave normalization off when the original amplitude scaling is already correct.
The residual measures the gap between the measured response and the reconvolved estimate. Smaller residuals usually indicate a better match, though overfitting can still hide inside noisy data.
Yes. After calculation, use the CSV button for spreadsheet work or the PDF button for reports, reviews, and client-facing documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.