PERIODIC ANALOG SIGNALS

Periodic analog signals can be classified as simple or composite. A simple periodic analog signal, a sine wave, cannot be decomposed into simpler signals. A composite periodic analog signal is composed of multiple sine waves.

Topics discussed in this section:

• Sine Wave
• Wavelength
• Time and Frequency Domain
• Composite Signals
• Bandwidth

A sine wave

A sine wave can be represented by three parameters: the peak amplitude, the frequency, and the phase. These three parameters fully describe a sine wave.

Amplitude

The peak amplitude of a signal is the absolute value of its highest intensity, proportional to the energy it carries. For electric signals, peak amplitude is normally measured in volts.

Period and Frequency

Period refers to the amount of time, in seconds, a signal needs to complete 1 cycle.Frequency refers to the number of periods in I s.

Phase

The term phase describes the position of the waveform relative to time 0. Phase is measured in degrees or radiant

Note

Frequency and period are the inverse of
each other.

Units of period and frequency

Note

Frequency is the rate of change with

respect to time.

Change in a short span of time

means high frequency.

Change over a long span of

time means low frequency.

Note

If a signal does not change at all, its

frequency is zero.

If a signal changes instantaneously, its

frequency is infinite.

Note

Phase describes the position of the

waveform relative to time 0.

Wavelength

Wavelength is another characteristic of a signal traveling through a transmission medium. Wavelength binds the period or the frequency of a simple sine wave to the propagation speed of the medium. The wavelength is the distance a simple signal can travel in one period.

Wavelength can be calculated if one is given the propagation speed (the speed of light) and the

period/frequency of the signal. we represent wavelength by A, propagation speed by c (speed of light), and frequency by 1, we get

Time and Frequency Domains

• To show the relationship between amplitude and frequency, we can use what is called a frequencydomain plot.
• A frequency-domain plot is concerned with only the
• Peak value and the frequency. Changes of amplitude during one period are not shown.
• Figure 7 shows a signal in both the time and frequency domains.

The time-domain and frequency-domain plots of a sine wave

Note

A complete sine wave in the time

domain can be represented by one

single spike in the frequency domain.

The time domain and frequency domain of three sine waves

Note

A single-frequency sine wave is not

useful in data communications;

we need to send a composite signal, a

signal made of many simple sine waves.

Composite Signals

• Any composite signal is actually a combination of simple sine waves with different frequencies, amplitudes, and phases.
• A composite signal can be periodic or non-periodic.
• A periodic composite signal can be decomposed into a series of simple sine waves with discrete frequencies.
• Frequencies that have integer values (1, 2, 3, and so on).
• A non-periodic composite signal can be decomposed into a combination of an infinite number of simple sine waves with continuous frequencies, frequencies that have real values.

Note

If the composite signal is periodic, the

decomposition gives a series of signals

with discrete frequencies;

if the composite signal is non-periodic,

the decomposition gives a combination

of sine waves with continuous

frequencies.

A composite periodic signal

Decomposition of a composite periodic signal in the time and frequency domains

The time and frequency domains of a nonperiodic signal

Bandwidth

• The range of frequencies contained in a composite signal is its bandwidth.
• The bandwidth is normally a difference between two numbers. For example, if a composite signal contains frequencies between 1000 and 5000, its bandwidth is 5000 - 1000, or 4000.

Note

The bandwidth of a composite signal is

the difference between the

highest and the lowest frequencies

contained in that signal.

The bandwidth of periodic and non-periodic composite signals