2.5 Problems

2.5 Problems

1. 

In a PAL system, determine the values of the three colour primaries R, G and B for the following colours: red, green, blue, yellow, cyan, magenta and white.

 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. 

Calculate the luminance and chrominance values of the colours in problem 1, if they are digitised into eight bits, according to CCIR-601 specification.

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

3. 

Calculate the horizontal scanning line frequency for CCIR-601/625 and CCIR-601/525 line systems and hence their periods.

 and

4. 

CCIR-601/625 video is normally digitised at 13.5 MHz sampling rate. Find the number of pixels per scanning line. If there are 720 pixels in the active part of the horizontal scanning, find the duration of horizontal scanning fly-back (i.e. horizontal blanking interval).

 ; 864 - 720 = 144 pixels;

5. 

Repeat problem 4 for CCIR-601/525.

857 pixels; 857 - 720 = 137 pixels; 10 s

6. 

Find the bit rate per second of the following video formats (only active pixels are considered):

  1. CCIR-601/625; 4:2:2

  2. CCIR-601/525; 4:2:2

  3. SIF/625; 4:2:0

  4. SIF/525; 4:2:0

  5. CIF

  6. SIF/625; 4:1:1

  7. SIF/525; 4:1:1

  8. QCIF(15 Hz)

  9. subQCIF(10 Hz)

 a. 720 576 25 2 8 = 166 mbit/s b. 720 480 30 2 x 8 = 166 mbit/s c. 360 288 25 1.5 8 = 31 mbit/s d. 360 240 30 1.5 8 = 31 mbit/s e. 37 mbit/s f. 31 mbit/s g. 31 mbit/s h. 4.7 mbit/s i. 1.4 mbit/s

7. 

The luminance values of a set of pixels in a CCIR-601 video are: 128; 128; 128; 120; 60; 50; 180; 154; 198; 205; 105; 61; 93; 208; 250; 190; 128; 128; 128. They are filtered and downsampled by 2:1 into SIF format. Find the luminance values of seven SIF samples, starting from the fourth pixel of CCIR-601.

94 73 194 184 50 204 207

8. 

The luminance values of the SIF pixels in problem 7 are upsampled and filtered into CCIR-601 format. Find the reconstructed CCIR-601 format pixel values. Calculate the PSNR of the reconstructed samples.

94 82 73 132 194 201 184 109 50 121 204 222 207 psnr = 20.2 db

9. 

A pure sinusoid is linearly quantised into n bits:

  1. show that the signal-to-quantisation noise ratio (SNR) in dB is given by SNR = 6n + 1.78,

  2. find such an expression, for peak SNR (PSNR),

  3. calculate the minimum bit per pixel required for quantising video, such that PSNR is better than 58 dB.

    hint: 

    (the mean-squared quantisation error of a uniformly quanitised waveform with step size Δ is Δ2/12).

 a. a sinusoid with amplitude a has a peak-to-peak 2a = 2 n ∆ → ∆ a = a 2 1- n b. peak-to-peak power of the sinusoid is higher than its mean power → psnr = 10.78 + 6n c. 10.78 + 6 n ≥ 58 → n ≥ 8 bits

Answers

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 21-n

    click to expand

  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



Standard Codecs(c) Image Compression to Advanced Video Coding
Standard Codecs: Image Compression to Advanced Video Coding (IET Telecommunications Series)
ISBN: 0852967101
EAN: 2147483647
Year: 2005
Pages: 148
Authors: M. Ghanbari

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