DIGITAL SIGNALS

DIGITAL SIGNALS

In addition to being represented by an analog signal, information can also be represented by a digital signal.
For example, a 1 can be encoded as a positive voltage and a 0 as zero voltage.
A digital signal can have more than two levels.
In this case, we can send more than 1 bit for each level.

Two digital signals: one with two signal levels and
the other with four signal levels

Examples

A digital signal has 8 levels. How many bits are needed per level?

We calculate the number of bits from the formula


Each signal level is represented by 3 bits.

A digital signal has 9 levels. How many bits are needed per level?

Each signal level is represented by 3.17 bits.
The number of bits sent per level needs to be an integer as well as a power of 2.
Hence, 4 bits can represent one level.

Example

HDTV uses digital signals to broadcast high quality video signals. There are 1920 by 1080 pixels per screen, and the screen is renewed 30 times per second. Also, 24 bits represents one color pixel.
What is the bit rate for high-definition TV (HDTV)?


The TV stations reduce this rate to 20 to 40 Mbps through compression.


Baseband transmission

A digital signal is a composite analog signal with an infinite bandwidth.


Baseband transmission using a dedicated medium

Baseband transmission of a digital signal that preserves the shape of the digital signal is possible only if we have a low-pass channel with an infinite or very wide bandwidth.


Example

An example of a dedicated channel where the entire bandwidth of the medium is used as one single channel is a LAN.
Almost every wired LAN today uses a dedicated channel for two stations communicating with each other.
In a bus topology LAN with multipoint connections, only two stations can communicate with each other at each moment in time (timesharing); the other stations need to refrain from sending data.
In a star topology LAN, the entire channel between each station and the hub is used for communication between these two entities.


Example

What is the required bandwidth of a low-pass channel if we need to send 1 Mbps by using baseband transmission?
Solution
The answer depends on the accuracy desired.
a. The minimum bandwidth, is B = bit rate /2, or 500 kHz.
b. A better solution is to use the first and the third harmonics with B = 3 × 500 kHz = 1.5 MHz.
c. Still a better solution is to use the first, third, and fifth harmonics with B = 5 × 500 kHz = 2.5 MHz.


Example

We have a low-pass channel with bandwidth 100 kHz. What is the maximum bit rate of this channel?
Solution
The maximum bit rate can be achieved if we use the first harmonic. The bit rate is 2 times the available bandwidth, or 200 kbps.

Bandwidth of a bandpass channel

If the available channel is a bandpass channel, we cannot send the digital signal directly to the channel; we need to convert the digital signal to an analog signal before transmission.


Modulation of a digital signal for transmission
on a bandpass channel

An example of broadband transmission using modulation is the sending of computer data through a telephone subscriber line, the line connecting a resident to the central telephone office.
These lines are designed to carry voice with a limited bandwidth.
The channel is considered a bandpass channel.
We convert the digital signal from the computer to an analog signal, and send the analog signal.
We can install two converters to change the digital signal to analog and vice versa at the receiving end.
The converter, in this case, is called a modem