Tài liệu Lecture 14: The Theoretical Basis for Data Communication: pptx

The Theoretical Basis for Data Communication: Frequency-domain concept: A sine wave with a frequency of 1 kHz will look like this in the frequency domain: Signal Amplitude, A Frequenc

The Theoretical Basis for Data Communication:

Frequency-domain concept:

A sine wave with a frequency of 1 kHz will look like this in the frequency domain:

Signal

Amplitude,

A

Frequency, f

1 kHz

Fourier Theorem:

In the early 19th century, the French mathematician Jean-Baptiste Fourier states that:

Any periodic waveform can be expressed as the sum of sine waves with frequencies at integer or harmonic multiples of the fundamental frequency of the waveform and with appropriate maximum amplitudes and phases

A square wave of 1 kHz is composed of a 1 kHz sine wave and its odd multiples (Harmonics) with diminishing amplitudes:

A Sin(2π(f1)t) + A/3 sin(2π(3f1)t) + A/5 sin(2π(5f1)t) + A/7 sin(2π(7f1)t)

Signal

Amplitude,

A

Frequency, f

1 kHz

Reed organ is also called Harmonica, as the reeds are tuned to vibrate at harmonics of the fundamental signal

Addition of Frequency Components:

Addition of More Frequency Components:

Voice signal:

Voice signal is an analog signal with frequency components in the range of 20Hz to 20kHz:

Signal

Amplitude,

A

Time, t Voice signal

Signal

Amplitude,

A

Frequency, f

Spectrum, of a signal is the range of frequencies that it contains The intelligent voice signal spectrum

extends from 300 Hz to 3400 Hz

Bandwidth, of a signal is the width of the spectrum The bandwidth of the intelligent voice signal is

3100 Hz

Telephone equipment allows the voice a bandwidth of 4000Hz, which includes a guard band at top (600Hz) and bottom (300Hz) to prevent interference This limit on bandwidth is imposed by the telephone and the switching equipment used in the telephone network

Video signal:

Video signal is an analog signal with frequency components in the range of 60 Hz to 4 MHz

The bandwidth is almost 4 MHz With guard bands the standard bandwidth for colour video signaling

is 6 MHz

Digital Data Signal:

Bit rate, is the number of bits transmitted per second

Baud rate, is the signaling speed That is the number of times the signal changes its value , e.g., voltage per second

In case of digital transmission through the transmission line similar to telephone line of bandwidth 3.1 kHz the maximum bits can be transmitted is 3.1 kHz x 2 = 6.2 kbps

But in practice we transmit through the telephone lines either tones (1200Hz) of different amplitude or two different tones (1200Hz & 2400Hz) to represent 0 and 1 per unit time of the signal So, the

maximum bit rate is the same as the signal rate, 3.1 kbps

To increase the bit rate different coding scheme has been implemented over time That is 2, 4, 8 and 16 bits has been transmitted per signal unit So, the baud rate and the bit rate are no longer the same

Power in Telecommunications and Decibels:

Power is the amount of energy per unit time and is unit is Watts

1 W of electricity is equal to 1 A of electricity flowing through 1 Ohm of resistance

P = I2 R

If current is doubled, the power goes up by a factor of 4

In telecommunications, we deal with extremely low power levels such as 10 thousandth of a watt (10 mW)

The milliwatt is the unit of measure used for power in telecommunications circuits

Rather than absolute measure of power, we often concerned with the comparison of one power level to another

Such as the output power of an amplifier (RF or AF) is 1000 mW for an input power of 10 mW

We can say this whole this output with one unit, such as the output is 20dB

The relative power of output to input will tell us the gain of the amplifier, Po/PI = 1000mW/10mW

= 100

The unit of measure used to compare two power levels is the decibel (dB)

A decibel is not an absolute measurement It is a relative measurement The decibel level indicates the relationship of one power level to another

The formula for calculating decibel is :

dB = 10 log Po/Pi

= 10 log 1000mW/10mW

= 10 log 100

= 10 x 2

dB tells us the ratio of two power levels, that is it expresses the gain of the system

But some time we want to express the exact output power of a system rather than the gain

In that case, we compare the power levels with a known reference, such as 1mW

So, the output power will be 30 dBm (10 log 1000mW/1mW = 10 x log 1000 = 10 x 3)

Notice the addition of a small "m" after the "dB", that says the reference is 1 mW

Decibels referenced to 1 mW provides a convenient measure for measuring the signal levels in

telecommunications because most signal levels in the telecommunications system fall within +10 and

-10 dBM i.e., -10 mW to -100 microW

Signal-to-Noise Ratio:

The term Signal-to-Noise ratio is used to express in decibels how much higher in level a signal is to the noise on the circuit

In telecommunications, a Signal-to-Noise ratio of 30 dB or more is satisfactory

Signal-to-Noise ratio = signal level in dBm - noise level in dBm

So, for a 10 dBm signal (10 mW) the noise level has to be less than -20 dBm (10 microW)

Shanon Theorem:

Mathematical guidelines have been established to determine the maximum theoretical data transfer over a channel based on the channel's bandwidth and Signal-to-Noise ratio This is known as the

channel capacity (maximum number of bits per sec)

One of the most fundamental laws used in telecommunications is Shanon's law

In 1948 Shanon proved that the maximum data rate of a noisy channel whose bandwidth is B Hz, and whose signal-to-noise ratio is S/N, is given by

Channel Capacity = B log2 (1+S/N) bps

For a bandwidth of 3.1 kHz and a signal to noise ratio of 30 dB (a ratio of 1000/1),

the maximum data rate is 31 kbps

Channel Capacity = B log2 (1+S/N) bps

= 3100 log2 (1+1000) bps

= 3100 log2 (1001) bps

= 3100 log2(29.967) bps

= 3100 x 9.967 bps

= 30,898 bps

= 31 kbps Todays Modems reached that limit of data rate on a old telephone line (it is not the wire itself, it

includes the circuitry at the local telephone offices)