Problems

1) How do we achieve a data rate of 56 kbps in 23 channels using DS-1 format?

There are 24 voice channels on a DS-1. One of them is used for in digital transmission for synchronization. That leaves us with 23 channels.

There are 8 bits per channel. One of them is used to for control information. That leaves us with 7 bits.

So, each remaining 23 channels gets 7 bits, 8000 samples per second (voice sampling rate) for a channel rate of (7 bits * 8000 sample p/s) or 56 kbps.

3) A scanner provides 1200dpi resolution over 1 billion colors.

1. Memory in bytes to store a bit map of an 8 * 10 in. monochrome picture at 1200 dpi with a 10-bit gray scale?

1200 * 1200= 1,440,000

8 * 10 * 1,440,000 * 10 bit = 144,000,000 bytes

2. The colors are red, blue, and green. What is the least value of n that will provide over 1 billion colors?

Red=10 bits

Blue=10 bits

Green=10 bits

10 * 10 * 10 = 1000 or 2 ³⁰

3. How long would it take to send a 8*10 in. picture at 1200 dpi over a T-1 line?

8 * 10 * 1,440,000 * 30 bits = 3,456,000,000 / 1,000,000 = 3,456 Mb / 1.544 Mbps = 2,238 sec

4) The photoprinter resolution is 2400 dpi. Suppose that you want to send a 7*11 inch page of material.

1. If you store it, uncompressed, as pixels in your PC, how much memory do you need in bytes?

7 * 11 = 77 * (2400 * 2400) = 443,520,000 bytes = 55,440,000

2. If a modem transmits at 19,200 bps. How long would it take to send the file to the typesetter?

443,520,000 / 19,200 = 23,100 /3600 = 6.42 hours

5) Assume that you are to design a TDM carrier, say T-489, to support 30 voice channels using 6-bit samples and structure similar to T-1. Determine the bit rate required.

(30 * 6) + 1 = 181 bits * 8000 = 1.448 mbps