representation of signals and systems (chapter iii)

1 /26 INFORMATION TECHNOLOGY Seppo Horsmanheimo21/04/23

Representation of Signals Representation of Signals and Systemsand Systems(Chapter III)(Chapter III)

Simon Haykin, Communication Systems


Wake-up jokesWake-up jokes C'mon baby, do the locomotion with me - tule lapsi, tee minulle höyryveturi Rock me baby - kivitä lastani Love me tender - rakasta hampaitani/rakasta minua hiilivaunussa Undressed custom model - Tullin alastonmalli Manicure - Raha parantaa I have been there - Minulla on papu siellä To be or not to be? - Ampiaiselle vai ei? We are the champs - Olemme herkkusieniä Do you feel allright? - Tunnetko kaikki oikealta? Bye bye baby, baby goodbye - Osta osta vauva, vauva hyvä ostos I fell in love - Kompastuin rakkaaseen Just in case - Vain salkussa I will never give up - En koskaan oksenna Oh dear - Voi peura I saw my Honey today - Sahaan hunajaani tänään I'm going to make you mine - Menen tekemään sinulle kaivoksen Carpet factory - Autolemmikkitehdas Bad influence - Paha räkätauti Holiday with son - Harley Davidson Press space bar to continue - Lehdistö avaruusbaariin jatkoille


Things to talk aboutThings to talk about

Amplitude modulation (AM) Limitations and improvements of AM Different kinds of modulations FDM Frequency-division Multiplexing Angle modulation Transmission of FM signals FM stereo multiplexing PLL-system Superheterodyne receiver


Continuous Wave ModulationContinuous Wave Modulation The purpose of communication channel is to transmit information-

bearing signals or baseband signals through a communication channel separating the transmitter from the receiver.

Baseband is the band of frequencies representing the original signal. The utilization of communication channel requires a shift of the range

of baseband frequencies into other frequency ranges suitable for transmission, and a corresponding shift back to the original frequency range after reception.

This shift is accomplished by using modulation. Modulation is defined as the process by which some characteristic of a

carrier is varied in accordance with a modulating wave. Modulation is performed at the transmitting end of the communication

system. After receiving a signal original baseband signal is restored by using

demodulation. Demodulation is the way to restore the original baseband signal.


Continuous Wave ModulationContinuous Wave Modulation Two modulation techniques:

Amplitude modulation (amplitude is varied), Angle modulation (angle is varied).

Amplitude modulation is the oldest modulation method. It is cheap to build (AM broadcasting). Let’s analyze a sinusoidal carrier wave c(t)

)2cos()( tfAtc cc where Ac is carrier amplitude and fc is carrier frequency. Let m(t) denote the baseband signal that carries the message. AM is defined as a process in which the amplitude of the carrier wave

c(t) is varied about a mean value. An amplitude-modulated signal can be described as a function of time.

)2cos()(1)( tftmkAts cac where ka is defined as amplitude sensitivity of the modulator

responsible for the generation of the modulated signal s(t).


Amplitude modulationAmplitude modulation The envelope of s(t) has same shape as the baseband signal m(t)

provided that two requirements are satisfied:

1. |kam(t)| < 1 for all t,

2. Fc >> W, W is the message bandwidth. If first requirement says that s(t) must always be positive. If this is not

satisfied the carrier wave becomes overmodulated. Whenever the factor 1+kam(t) crosses zero, phase reversals happens.

Thus the modulated wave exhibits envelope distortion. The maximum value of kam(t) multiplied by 100 is referred as

percentage modulation and it should be less than 100.Example ofBaseband signal m(t)


1st requirement1st requirement

|kam(t)| < 1 |kam(t)| > 1


2nd requirement2nd requirement

Fc >> W Fc < W


AM detectionAM detection A simple and highly effective demodulation device is envelope

detector.

It consists of a diode and resistor – capacitor filter. First the diode is forward-biased and the capacitor C charges up rapidly to peak value. When input signal false below this value, the diode becomes reverse-biased and the capacitor C discharges slowly through the load resistor Rl.


AM Limitations and ImprovementsAM Limitations and Improvements AM has two major limitation:

1. Amplitude modulation is wasteful of power (only a fraction of the total transmitted power is affected by m(t).

2. Amplitude modulation is wasteful of bandwidth (it requires a transmission bandwidth equal to twice the message bandwidth)

These limitations can be overcome using:1.Double sideband-suppressed carrier (DSB-SC) modulation,2.Vestigial sideband (VSB) modulation, 3. Single sideband (SSB) modulation.

In DSB-SC transmitted power is saved through the suppression of the carrier wave, the channel bandwidth is still the twice the message bandwidth.

The modulated signal s(t) undergoes a phase reversal whenever the message m(t) crosses zero.


DSB-SC generator and demodulatorsDSB-SC generator and demodulators DSB-SC wave can be generated with ring modulator that contains

four diodes pointing in the same direction. Demodulation of DSB-SC signal can be done by Coherent Detection

or Costas receiver.

In Costas receiver the upper path is referred to as the in-phase coherent detector (I-channel) and the lower path is referred to as the quadrature-phase coherent detector (Q-channel). These detectors are coupled together to form a negative feedback system.


Quadrature-Carrier MultiplexingQuadrature-Carrier Multiplexing in QAM-system the transmitter part of the system uses two separate

product modulator that are supplied with two carrier waves of the same frequency but which differ in phase –90 degrees.

For the system to work, the correct phase and frequency relationships between the local oscillators must be maintained.

by Costas receiver, by use of a pilot signal outside the modulated signal.

QAM-transmitter QAM-Receiver


Vestigial SidebandVestigial Sideband In Vestigial sideband (VSB) modulation the one sideband is passed

almost completely and the vestige of the other sideband is retained. It is suitable for wideband signals like TV signal. Bandwidth is close to the message bandwidth.

The cutoff portion of the frequency response around the carrier frequency fc exhibits odd symmetry.

fv is the width of vestigial sideband.


TV Broadcasting uses VSBTV Broadcasting uses VSB Reasons:

1. The video signal has a large bandwidth and significant low-frequency content.

2. The circuitry used for demodulation in the receiver must be simple and cheap.

The VSB filter is inserted in each receiver where the power levels are low.

Typically video signal and voice has own carrier signals.

The distortion of VSB modulated signal can be reduced by: By reducing the percentage modulation to reduce the amplitude

sensitivity ka,

By increasing the width of the vestigial sideband to reduce m'(t).


Single Sideband ModulationSingle Sideband Modulation In Single Sideband (SSB) modulation the modulated signal contains

only the upper or lower sideband. It is suitable for transmitting voice due to energy gap that exists in the

spectrum of voice signal between zero and a few hundred Herz. Benefits:

Minimum transmission power, Minimum channel bandwidth.

For generation of an SBB modulated wave, the following requrements must be satisfied:

1. The desired sideband lies inside the passband of the filter,2. The unwanted sideband lies inside the stopband of the

filter,3. The filter's transition band (between passband and

stopband) must be twice the lowest frequency component of the message signal.


Single Sideband ModulationSingle Sideband Modulation

In practice it is necessary to generate SBB signal occupying a frequency band that is much higher than that of the baseband signal.

This can be done by using multiple modulation process. Demodulation SSB requires perfect synchronization of phase and

frequency.

This can be achieved by: Transmitting a low-power pilot carrier, Using a highly stable oscillator tuned to same frequency as the carrier

frequency.


Frequency-Division Multiplexing Frequency-Division Multiplexing The idea is to combine a number of independent signals into a

composite signal suitable for transmission over a common channel. To transmit a number of these signals over the same channel, the

signals must be kept apart so that they do not interfere with each other. There are two ways to do it:

Frequency-division multiplexing, FDM where signals are separated in frequency.

Time-division multiplexing, TDM where signal are separated in time.

FDM takes three steps:1. high-frequency components are removed by low-pass

filter,2. signal is shifted to mutually exclusive frequency intervals

by modulators (SSB),3. the band-pass filter is used to restrict the band of each

modulated wave to its prescribed range.


Frequency-Division MultiplexingFrequency-Division Multiplexing Used in telephone systems.

At receiver the signal is handle in inverse order. To provide two-way transmission the system must be duplicated to

provide communication also to the other direction.


Angle ModulationAngle Modulation It is the other way to modulate signal. It modulates the angle of the carrier wave. It provides better discrimination against noise and interference. An angle-modulated signal can be expressed as

)(2)( tmktft pci

)(cos)( tAts ic

Where Ac is carrier amplitude. The complete oscillation occurs whenever i(t) changes 2. Two common ways in which i(t) varies:

In Phase Modulation (PM) the angle i(t) is varied linearly with the message signal m(t)

The term 2 fc represents the unmodulated carrier and kp represents the phase sensitivity of the modulator.


Angle ModulationAngle Modulation In Frequency modulation (FM) the instantaneous frequency fi(t) is

varied linearly with the message signal m(t)

PM and FM signal have no longer a perfect regularity in their spacing; zero crossings refer to the instants of time at which a waveform changes from a negative to a positive value or vice versa.

The other important difference is that the envelope of PM or FM is constant whereas the envelope of an AM signal is dependent on the message signal.

The term fc is the frequency of the unmodulated carrier and the constant kf is the frequency sensitivity.

)()( tmkftf fci


Angle ModulationAngle Modulation


Transmission of FM SignalsTransmission of FM Signals In theory a FM signal contains an infinite number of side frequencies

so that the bandwidth required to transmit such a signal is similarly infinite.

In practice the FM signal is effectively limited to a finite number of significant side frequencies compatible with a specified amount of distortion.

There is an approximate rule for the transmission bandwidth of an FM signal generated by a single-tone modulating signal of frequency fm

where is the modulation index and f is the frequency deviation. This empirical relation is known as Carson's rule.

)1

1(222

fffB mT


Generation and demodulationGeneration and demodulation FM signal generation can be done directly or indirectly. In direct generation the instantaneous frequency of the carrier wave is

varied directly with the message signal by voltage-controlled oscillator.

In indirect generation the message signal m(t) is integrated and then used to phase-modulate a crystal-controlled oscillator.

FM signal demodulation can be done directly or indirectly. Direct demodulation uses frequency discriminator whose amplitude

is directly proportional to frequency of input FM signal. Frequency discriminator consists of a slope circuit followed by an

envelope detector.


FM Stereo MultiplexingFM Stereo Multiplexing Is a form of a FDM is designed to transmit two separate signals via the

same carrier. It is widely used in FM radio broadcasting to send two different

elements of a program so as to give a spatial dimension to its perception by a listener.

FM Stereo transmission has to follow two principles:1. It has to operate within the allocated FM broadcast

channels,2. It has to be compatible with monophonic radio receivers.


Phase-locked loopPhase-locked loop PLL is a negative feedback system. It can be used for:

synchronization, frequency division/multiplication, indirect frequency demodulation.

It contains: a multiplier, a loop filter, voltage-controlled oscillator (VCO).

They are connected together in the form of feedback loop.


Superheterodyne receiverSuperheterodyne receiver

In addition to demodulating the incoming modulated signal, receiver may have other tasks like:

Carrier-frequency tuning (to select the desired signal), Filtering (to separate the desired signal from the other modulated

signals that are picked up along the way, Amplfication (to compensate for the loss of signal power incurred in

the course of transmission, Superheterodyne or superhet is referred to a receiver that does all

those tasks. Today all radio and TV receivers are superheterodyne receivers.

representation of signals and systems (chapter iii)

Documents

amplitude modulation

carrier amplitude

original signal

amplitudemodulated signal

baseband signal mt

carrier frequency

baseband signals

angle modulation angle