Data & Signals

Analog & digital
Periodic analog signal
Digital signal
Transmission Impairment
Data rate limits
Performance
Physical Layers
Bit-to-Signal Transformation

To be transmitted, data must be transformed to electromagnetic signals.
Bit-Rate Control
The transmission medium provides the upper limit on data rate, the physical layer controls it
Bit Synchronization
The physical layer provides clocking mechanisms to control the timing of bit transfer
Multiplexing
A physical link may need to be divided into logical channels, each used by a transmission, for better efficiency
Circuit Switching
Allowing pairs of nodes to have their dedicated links is a function of the physical layer
Analog and Digital Signals
Signals can be analog or digital. Analog signals can have an infinite number of values in a range; digital signals can have only a limited number of values.

In data communications, we commonly use periodic analog signals and aperiodic digital signals.
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.

Phase

Question: A sine wave is offset one-sixth of a cycle with respect to time zero. What is its phase in degrees and radians???
Sine Wave: One more example
An analog signal is best represented in the frequency domain.

Use of Sine Waves

A power company sends a single sine wave with frequency 60Hz to distribute electric energy to houses and businesses
We can use a single sine wave to send an alarm to a security center
But single sine waves are useless in data communications. WHY?
Think about phone conversation

Composite Analog Signals

In reality, signals are more complicated than sine waves => can be represented as a combination of sine waves with different frequencies, amplitude, and phases
(using Fourier transformation)

Fourier Transformation

s(t)=A1sin(2f1t+ф1) + A2sin(2f2t+ф1) + A3sin(2f3t+ф3) +…

Frequency Spectrum

The description of a signal using the frequency domain and containing all its sine-wave components is called the frequency spectrum of that signal

Signal Over Transmission Medium

Signal corruption: Transmission medium may block or weaken some frequencies. As a result, the output signal may be different from the input signal.
Perfect medium: preserve frequency, amplitude, and phase values

Bandwidth of Transmission Medium

The bandwidth is a property of a medium: It is the difference between the highest and the lowest frequencies that the medium can satisfactorily pass.


Digital vs. Analog

Digital’s advantage:
Digital design less expensive and more reliable
Greater dynamic range and error detection and recovery by the use of coding
Many sources can be combine (voice, video, data) and sent over the same channel
Digital’s disadvantage
More bandwidth needed

Baseband vs. Broadband Signals

Baseband signal: frequency spectrum extends from 0 to some maximum frequency (similar to low-pass channel’s property)
Broadband signal: frequency spectrum belongs to a range between a min freq and a max freq (similar to band-pass channel’s property)


Data Rate Limits

How fast can we send data (in bps) over a link?
The answer depends on
Bandwidth available
Levels of signals we can use
Quality of channel (level of noise)


Noiseless Channel: Nyquist Bit rate


Bit Rate = 2  Bandwidth  log2L
L: the number of signal levels used to represent data

Noisy Channel: Shannon Capacity

Channel Capacity = Bandwidth  log2(1+SNR)
SNR: signal to noise ratio – statistical ratio of the signal power and noise power
Bandwidth: analog channel bandwidth



Bit Rate = 2  3000  log2 2 = 6000 bps