8/23/09

ANALOG AND DIGITAL

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

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.


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.


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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