College

Assume 8 bits = 1 Byte. A movie has the following video and audio specifications:

**Video specifications:**
- Resolution: 1200 x 900 pixels
- Color depth: 24 bits/pixel
- Frame rate: 30 fps

**Audio specifications:**
- Sample rate: 50 kHz
- Number of bits/sample: 1 Byte/sample
- Stereo

a) Calculate the data rate of the video only.

b) Calculate the data rate of the audio only.

c) Determine the total data size of the video and audio if the duration is 12 minutes and 5 seconds.

d) If the video and audio are compressed with a compression ratio of 25:1, calculate:
(i) The new data size
(ii) The time taken to transmit the compressed video and audio over a network with a line speed of 100 Mbps.

Answer :

a) Calculate the data rate of the video only.Data rate of the video only = Frame size x Frame rateFrame size= (1200 x 900 pixels) x 24 bits/pixel= 31,104,000 bitsFrame rate = 30 fps

Data rate of the video only = 31,104,000 x 30 bits/sec= 933,120,000 bits/sec1 Byte = 8 bitsData rate of the video only = 933,120,000/8 Bytes/sec= 116,640,000 Bytes/secb)

Calculate the data rate of the audio only. Data rate of the audio only = Sample rate x Number of bits/sample x No. of channels Sample rate = 50 KHz

Number of bits/sample = 8 bits (1 Byte/sample)No. of channels = 2 (Stereo)Data rate of the audio only = 50,000 samples/sec x 8 bits/sample x 2= 800,000 bits/sec1 Byte = 8 bits

Data rate of the audio only = 800,000/8 Bytes/sec= 100,000 Bytes/sec

Determine the total data size of the video+audio, if the duration is 12 minutes 5 seconds.

Total data size of the video+audio = (data rate of video only + data rate of audio only) x durationDuration of the video+audio = 12 minutes 5 seconds= 725 seconds

Total data size of the video+audio= (116,640,000 Bytes/sec + 100,000 Bytes/sec) x 725 sec= 84,563,600,000 Bytes= 84.56 GBd)

If the video+audio is compressed with a compression ratio of 25:1, calculate its new data size and the time taken to transmit the compressed video+audio over a network with a line speed of 100 Mbps.(i) New data size = Total data size of the video+audio/Compression ratio= 84,563,600,000 Bytes/25= 3,382,544,000 Bytes= 3.38 GB

(ii) Time taken to transmit the compressed video+audio over a network with a line speed of 100 Mbps.

Data transmission rate= 100 Mbps= 100,000,000 bits/sec

Total data size of the video+audio = 3.38 GB= 3.38 x 1024 x 1024 x 1024 bytes= 3,629,512,243 bytes

Total time taken= Total data size/Data transmission rate= 3,629,512,243 bytes/100,000,000 bits/sec= 36.30 secondsTherefore, the time taken to transmit the compressed video+audio over a network with a line speed of 100 Mbps is 36.30 seconds.

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