main-written4solution

1: both defined for -1…17 f = – 2 2 2 0 0 0 4 4 4 0 0 0 2 0 2 0 2 –

1a. f * g = 2 -2 0 -2 2 0 4 -4 0 -4 4 0 2 -4 4 -4 4 -4 2

1b. f * h = -2 0 2 4 2 0 -4 0 4 8 4 0 -2 2 0 2 0 2 2

2: all defined for 0…7

2a. zero f * g(x) = 2 2 3 2 3 2 2 1

2b. clamp f * g(x) = 4 3 3 2 3 2 3 3

2c. mirror f * g(x) = 3 3 3 2 3 2 2 2 (3 2 3 2 3 2 3 2 is OK too but usually we want to mirror at the edge)

2c. mirror2 f * g(x) = 3 2 3 2 3 2 3 2

2d. re-norm f * g(x) = 10/3 5/2 3 2 3 2 5/2 5/3

3a. 1/25 *

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

3b.1/256 *

1 4 6 4 1

4 16 24 16 4

6 24 36 24 6

4 16 24 16 4

1 4 6 4 1

3c. 1/4 *

1 -1 2 -1 1

-1 1 -2 1 -1

2 -2 4 -2 2

-1 1 -2 1 -1

1 -1 2 -1 1

4: x 2.5 2.75 3 3.5

4a. box 0 4 4 4

4b. tent 2 3 4 4