Appendix F: Solutions to the Problems

Chapter 2

1. 	r	g	b	y	c	m	w
   R	1	0	0	1	0	1	1
   G	0	1	0	1	1	0	1
   B	0	0	1	0	1	1	1

2. 	r	g	b	y	c	m	w
   Y	82	145	41	210	170	107	235
   cb	90	54	240	16	166	202	128
   cr	240	34	110	146	16	222	128

3. and

4. ; 864 - 720 = 144 pixels;

5. 857 pixels; 857 - 720 = 137 pixels; 10 μs

6. 1. 720 × 576 × 25 × 2 × 8 = 166 Mbit/s

   2. 720 × 480 × 30 × 2 x 8 = 166 Mbit/s

   3. 360 × 288 × 25 × 1.5 × 8 = 31 Mbit/s

   4. 360 × 240 × 30 × 1.5 × 8 = 31 Mbit/s

   5. 37 Mbit/s

   6. 31 Mbit/s

   7. 31 Mbit/s

   8. 4.7 Mbit/s

   9. 1.4 Mbit/s

7. 94 73 194 184 50 204 207

8. 94 82 73 132 194 201 184 109 50 121 204 222 207 PSNR = 20.2 dB

9. 1. A sinusoid with amplitude A has a peak-to-peak 2A = 2ⁿ ∆ ⇒ ∆ A = A 2^1-n

      

   2. Peak-to-peak power of the sinusoid is

      

      higher than its mean power ⇒ PSNR = 10.78 + 6n

   3. 10.78 + 6n ≥ 58 ⇒ n ≥ 8 bits