Data Communications and

NetworksNetworksChapter 1: Bit rate and Modulation

Pham Quang Thai – pqthai.hcmut@gmail.com

1

Baud rate and bit rate

• 2-level signal: each symbol (voltage value)

represents “1” or “0”

• M-ary signal: each symbol (voltage value)

represents several “1” or “0”represents several “1” or “0”

• Bit rate is the number of bits per second

• Baud rate is the number of signal elements

(symbol) per second

• Baud rate ≤ bit rate

2logr L

NS

r

=

=

r

r: number of bits per symbol

L: number of levels (number of required symbols)

N: bit rate

S: baud rate (symbol per second)

Examples

1. A digital signal has eight levels. How many bits are needed

per level?

2. A digital signal has nine levels. How many bits are needed

per level?

Examples

3. A text documents is needed to sent at the rate of 100 pages

per minute. Each page has an average of 24 lines with 80

characters in each line. Assuming that one character requires

8 bits, what is the required bit rate of 2-level signal?

4. Voice signal’s bandwidth is 4 kHz. To send Internet voice call, 4. Voice signal’s bandwidth is 4 kHz. To send Internet voice call,

the signal is sampled at twice the highest frequency.

Assuming that each sample requires 8 bits, what is the

required bit rate of 2-level signal?

5. The HDTV signal is 1920 x 1080 pixels per screen. 24 bits

represents one color pixel. The screen is renewed 30 times

per second. What is the bit rate of 2-level signal?

Examples

6. An analog signal carries 4 bits per symbol. If 1000 symbols

are sent per second, find the bit rate.

7. An analog signal has a bit rate of 8000 bps and a baud rate of

1000 baud per second. How many bits are carried by each

symbol? How many symbol do we need?symbol? How many symbol do we need?

Modulation: needed when the medium is

bandpass or only a bandpass channel is

available

ASK’s bandwidth: B=(1+d)S

FSK’s bandwidth: B=(1+d)S+2Df

PSK’s bandwidth: B=(1+d)S

QPSK: M-ary version of PSK, 1 symbol

represents 2 bits

Constellation diagram: needed for

complex M-ary modulations

• Each symbol is a complex number and shown

as 1 dot in the constellation diagram

Example of constellation diagram

M-PSK’s bandwidth: B=(1+d)S

(noted that S=N/r)

Quadrature amplitude modulation (QAM):

M-ary modulation combines ASK and PSK

• M-QAM’s bandwidth: B=(1+d)S

(noted that S=N/r)

Examples

8. We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What are the carrier frequency and the bit rate if we modulated our data by using ASK with d = 1?

9. We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What should be the carrier from 200 to 300 kHz. What should be the carrier frequency and the bit rate if we modulated our data by using FSK with d = 1?

10. Find the bandwidth for a QPSK signal transmitting at 12 Mbps. The value of d = 0.

11. Find the bandwidth for a 16-PSK signal transmitting at 12 Mbps. The value of d = 0. Compare the result with the QPSK case.