**ANALOG AND DIGITAL**

Data can be analog or digital

Analog data refers to information that is continuous

Analog data take on continuous values

Analog signals can have an infinite number of values in a range

Digital data refers to information that has discrete states

Digital data take on discrete values

Digital signals can have only a limited number of values

**In data communications, we commonly use**

periodic analog signals and nonperiodic digital signals.

periodic analog signals and nonperiodic digital signals.

**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.

**Signal amplitude and Frequency**

*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.

If a signal does not change at all, its frequency is zero

If a signal changes instantaneously, its frequency is infinite.

Change in a short span of time means high frequency.

Change over a long span of time means low frequency.

If a signal does not change at all, its frequency is zero

If a signal changes instantaneously, its frequency is infinite.

**.**

Frequency and Period

Frequency and Period

Frequency and period are the inverse of each other.

**Phase**

Phase describes the position of the waveform

relative to time 0

**Wavelength and period**

Wavelength = Propagation speed x Period

= Propagation speed / Frequency

Time-domain and frequency-domain plots of a sine wave

A complete sine wave in the time domain can be represented by one single spike in the frequency domain.

Time-domain and frequency-domain plots of a sine wave

A complete sine wave in the time domain can be represented by one single spike in the frequency domain.

**Frequency Domain**

The frequency domain is more compact and useful when we are dealing with more than one sine wave.

A single-frequency sine wave is not useful in data communication

We need to send a composite signal, a signal made of many simple sine waves.

**Fourier analysis**

According to Fourier analysis,

any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.

If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies;

If the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.

**A composite periodic signal**

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

**Time and frequency domains of a nonperiodic signal**

A non-periodic composite signal

It can be a signal created by a microphone or a telephone set when a word or two is pronounced.

In this case, the composite signal cannot be periodic

because that implies that we are repeating the same word or words with exactly the same tone.

**Bandwidth**

The bandwidth of a composite signal is

the difference between the highest and the lowest frequencies contained in that signal.

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