Chapter 3

1. 1. |x| ≤ 16; y = 0 16 < |x| ≤ 32; y = ±24 32 < |x| < 48; y = ±40 etc.

   2. |x| ≤ 16; y = ±8 16 < |x| ≤ 32; y = ±24 32 < |x| ≤ 48; y = ±40 etc.

2. 12 16 28 240 196 32 PSNR = 43.4 dB

3. 6 12 27 77 127 77 PSNR = 10.7 dB

4. 15 21 19 21 19 69 119 169 219 234 232 230 232 230

   

5. 

6. 1. 364 15 -211 -26 -5 38 -2 -1

   2. the basis vector of the second AC coefficient matches the input pixels

   3. 35 82 190 250 200 150 101 23. Due to mismatch (approximating the cosine elements) some of the input pixels cannot be reconstructed, e.g. 81/82 and 100/101.

7. quantised coefficients:	360	0	-216	-24	0	40	0	0
   reconstructed pixels: PSNR = 30 dB	30	70	185	250	204	153	104	27

8. reconstructed pixels: PSNR = 10.4 dB	128	128	128	128	128	128	128	128
   reconstructed pixels: PSNR = 23.4 dB	28	87	169	227	227	169	87	28

9. 1. mv(-1, -1)

   2. mv(-1, -1)

10. 1. 169

    2. 1. multiplications = 256 × 169, additions = 511 × 169

       2. multiplications = 0, additions = 511 × 169

11. type	operations	Multiplications	additions
    TDL	23	23 × 256	23 × 511
    TSS	25	25 × 256	25 × 511
    CSA	17	17 × 256	17 × 511
    OSA	13	13 × 256	13 × 511

12. 1. = 010,

    2. = 1,

    3. = 00,

    4. = 011, av bits = 1.8, entropy = 1.72

13. 1. cbdad = 001011010011

    2. 1. 1st bit in error decoded string = babbad

       2. 3rd bit in error, decoded string = ccbbad

       3. 5th bit in error, decoded string = cbcbad

14. lower value = 0.83875, upper value = 0.841875

15. 1. the first three symbols = cbc

    2. the first five symbols = cbcab

16. the same as 15

17. 11010110111

18. the same as 17

19. 1. first bit in error = 0.01010110111 = 2^-2 + 2^-4 + 2^-6 + 2^-7 +2^-9 + 2^-10 + 2^-11 = 0.33935546875 which is decoded to string bbacb

    2. similarly, with the third bit in error the decimal number would be 0.96435546875, decoded to dbacb

    3. with the fifth bit in error, the decimal number is 0.87060546875 and it is decoded to string cbacb.