Filter design
A filter should be designed with a small mask and optimal smoothing properties. Use a mask with 3 coefficients: [α, β, γ]. The filter should have the following properties:
a) Preservation of the mean value
b) No shift of gray value structures
c) Structures with the largest possible wave number should vanish
Questions and tasks:
1. Are the filter coefficients α, β und γ determined uniquely?
2. Compute the transfer function of the filter
3. Which constraints are imposed to a filter with five coefficients [α, β, γ, δ, _]?
4. Compute the transfer function of the filter.
5. Which values can the remaining free parameter take so that the transfer function remains monotonically decreasing for all wave numbers?
6. Which coefficients have the corresponding filter masks for the limiting values?