1. Length-8 signal
Enter a signal $\vec u\in\mathbb R^8$. The tool computes the non-normalized fast Haar coefficients.
Threshold
2. Signal and reconstruction
Blue: original signal. Orange: reconstructed signal after thresholding.
3. Coefficient interpretation
The first coefficient is the average. The next coefficients describe coarse-to-fine details.
4. $2\times2$ image block
For $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$, compute average, vertical, horizontal, and diagonal Haar quantities.
5. Independent-study tasks with answers
Task A. Use the lecture example and threshold $2$. Which coefficients remain?
Answer: Coefficients with magnitude at least or greater than the chosen rule remain. In this tool, coefficients with $|c|<\tau$ are discarded.
Answer: Coefficients with magnitude at least or greater than the chosen rule remain. In this tool, coefficients with $|c|<\tau$ are discarded.
Task B. Create a piecewise constant signal. Which detail coefficients become zero?
Answer: Details inside constant adjacent pairs become zero. Larger-scale details are zero when larger blocks have the same average.
Answer: Details inside constant adjacent pairs become zero. Larger-scale details are zero when larger blocks have the same average.
Task C. For a constant $2\times2$ block, what are the non-average Haar quantities?
Answer: They are all zero.
Answer: They are all zero.