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.

Topics discussed in this section:

• Bit Rate
• Bit Length
• Digital Signal as a Composite Analog Signal
• Application Layer

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

Bit Rate

• Most digital signals are non-periodic, and thus period and frequency are not appropriate characteristics.
• Another term-bit rate (instead of frequency)-is used to describe digital signals.
• The bit rate is the number of bits sent in Is, expressed in bits per second (bps).

Bit Length

• The bit length is the distance one bit occupies on the transmission medium.
• Bit length = propagation speed x bit duration

Digital Signal as a Composite Analog Signal

• Based on Fourier analysis, a digital signal is a composite analog signal.
• A digital signal, in the time domain, comprises connected vertical and horizontal line segments.
• Fourier analysis can be used to decompose a digital signal.
• If the digital signal is periodic, which is rare in data communications, the decomposed signal has a frequency domain representation with an infinite bandwidth and discrete frequencies.
• If the digital signal is non-periodic, the decomposed signal still has an infinite bandwidth, but the frequencies are continuous.

The time and frequency domains of periodic and nonperiodic digital signals

Note

A digital signal is a composite analog

signal with an infinite bandwidth.

Transmission of Digital Signals

• We can transmit a digital signal by using one of two different approaches: base-band transmission or broadband transmission.
• Base-band transmission means sending a digital signal over a channel without changing the digital signal to an analog signal.
• Broadband transmission or modulation means changing the digital signal to an analog signal for transmission.

Base-band transmission

Base-band transmission using a dedicated medium

Note

Base-band 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.

Rough approximation of a digital signal using the first harmonic for worst case

Simulating a digital signal with first three harmonics

Note

In base-band transmission, the required

bandwidth is proportional to the bit rate;

if we need to send bits faster, we need

more bandwidth.

Bandwidth requirements

Bandwidth of a band-pass channel

Note

If the available channel is a band-pass

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 band-pass channel