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System model1.Design questions2.

Outline

Lecture #2Monday, January 13, 2014 9:52 AM

Introduction Pa e 1

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What are the big design challenges in the field of communications?

How is the impact of noise measured?

What are the properties of complex numbers?

IntroductionMonday, January 06, 2014 10:24 AM

Introduction Pa e 2

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Big design issuesWednesday, January 08, 2014 10:20 AM

Introduction Pa e 3

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Design questions:

What kind of signals are suitable for communictions?1.

How can the message

be recovered faithfully from

2.

Impact of the channel

Simplest type of a channel is called an additive noise channel.

Tuesday, January 07, 2014 4:30 PM

Introduction Pa e 4

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ExampleJanuary 8, 2014 11:42 AM

Introduction Pa e 5

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Decibel units1. Information rate2.

Lecture #3Thursday, January 09, 2014 6:54 PM

Introduction Pa e 6

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For many transmission channels, signal power commonly decays exponentially. Hencelog units make sense. Net gain (loss) across a cascaded systems can be calculated bysimple addition and subtraction.

DecibelsTuesday, January 07, 2014 6:11 PM

Introduction Pa e 7

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Note Decibel values refer to ratios, not absolute values. However, it is convenient to beable to refer to an absolute power expressed log units.

1 W reference:

1 mW reference.

Absolute levelsFriday, January 10, 2014 9:30 AM

Introduction Pa e 8

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What is the maximum information rate that can be transmitted through a channel?

Information rateTuesday, January 07, 2014 4:45 PM

Introduction Pa e 9

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Outline

Complex numbers1.Euler's formula2.

Lecture #4Monday, January 13, 2014 9:27 AM

Introduction Pa e 10

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Complex numbersTuesday, January 07, 2014 5:04 PM


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Euler's formulaTuesday, January 07, 2014 5:16 PM


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SummaryWednesday, January 08, 2014 10:27 AM


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Example: Simplify

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Main concepts

What is the energy of

?a.

What is the power of

? b.

What is the bandwidth of ?c.

Signal is a function of time - it can be complex or real1.

Fourier seriesa.Fourier transform b.Bandwidth computationc.

What is the Frequency domain representation of ?2.

What is happens when goes through a linear channel?3.

Lecture #5 1/15/2014

Common signals1.Periodic signals2.Energy of a signal3.Power of signals4.

Chapter 2Tuesday, January 07, 2014 6:13 PM

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Unit step function -

Unit rectangle function

Common signalsSaturday, January 11, 2014 12:20 PM

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Sinusoidal signal:

Complex sinusoid:

Periodic signal - repeats in time. Hence, it is enough to specify the signal in a basic interv

call the period. That is, there is a smallest such that


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Triangular signal

Sinc signal


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Impulse or Delta signal - for representing signals of very, very small duration

Sign (signum) signal

1.

2. For any continuous , we have


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The energy of a signal is the area under the squared signal.

Time (t)

Example: Find energy of (1) u(t) (2)

Energy signalsSaturday, January 11, 2014 1:25 PM

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Our definition of energy works well in many cases. However, what if the signal does notdecay? In this case we have infinite energy for any such signal.

Power is a time average of energy (energy per unit time). This is useful when the energyof the signal goes to infinity.

A signal cannot be both Power and Energy type. It is one or the other or neither.

Power signalsSaturday, January 11, 2014 1:35 PM

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Outline

Fourier series (real and complex versions)1. (Absolute) Bandwidth2. 3-dB bandwidth3.

Lecture #7Wednesday, January 15, 2014 2:55 PM

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Periodic functions - is of period

Where

Complex Fourier series

Periodic functions - is of period Where

plot as function of

is called the discrete spectrum of

Fourier SeriesSaturday, January 11, 2014 1:42 PM

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The absolute bandwidth of a signal is the difference between the highest and the lowestfrequencies (positive side only) contained in that signal.

Example:

BandwidthSunday, January 12, 2014 12:49 PM

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The previous definition is not meaningful sometimes because the range of positivefrequencies may be very broad or infinite.

Thus, this definition is typically relaxed so that the bandwidth is defined as the rangeof frequencies within which the power density is above half its maximum value (in

terms of the amplitude is more than of its maximum). Power ratio of 2 translates

to 3 dB.

Example:

3-dB BandwidthSunday, January 12, 2014 1:12 PM

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Outline

Fourier transform1. Signal classifications2. Bandwidth3.


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Main uses of Fourier transform (FT)

Fourier transformSaturday, January 11, 2014 1:54 PM

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A signal is said to be low-pass (or baseband) if

A signal is said to be band-pass if

Signal classificationWednesday, January 22, 2014 9:47 AM

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Low-pass signals -

the bandwidth is defined as the range of frequencies within which the power density

is above half its maximum value (in terms of the amplitude is more than

of its

maximum). Power ratio of 2 translates to 3 dB.

Alternative - f=0 to the first null = bandwidth

Bandpass signals

BandwidthSunday, January 12, 2014 1:12 PM

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Derive the FT of (1) Sketch the amplitude and phase spectrum.

ExamplesWednesday, January 15, 2014 2:59 PM

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Derive the FT of (1) Sketch the amplitude and phase spectrum.

ExamplesWednesday, January 15, 2014 2:59 PM

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Linearity1. Time scaling2. Time shifting3. Frequency shifting4.

Time-frequency duality5. Rayleigh's energy theorem6.

Properties of Fourier transform


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Linearity or superposition - Let the FT of and be and , then the FT o is

Time-scaling properity- Let the FT of be , then the FT of is

Example. Find the FT.

PropertiesWednesday, January 22, 2014 9:12 AM

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Time-shifting property: The FT of is PropertiesThursday, January 23, 2014 6:50 PM

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Frequency shifting1. Time-frequency duality2. Rayleigh's energy theorem3.

Properties of Fourier transform

Linear channels - distortion free- Band-pass

- low-pass


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Frequency-shifting property: The FT of is PropertiesThursday, January 23, 2014 6:50 PM

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Duality: The FT of is PropertiesThursday, January 23, 2014 6:50 PM

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Energy theorem :

Example. find the energy.

PropertiesThursday, January 23, 2014 6:50 PM

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Essential learning outcomes1. Review examples2. Written - Quiz (30 minutes)3.

Outline


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Describe the basic elements of communication systems,1.Define the quality of service parameters,2.Describe the impact of the resource constraints for communication systems,3.Use decibel notation to express power ratios and absolute power levels,4.

Quantify the impact of SNR and bandwidth increases on the maximum data rate,5.Perform magnitude and phase calculations on complex numbers,6.Use Euler's formula to simplify sine and cosine signals,7.Define common signals,8.Compute the energy, power and/or period of a given signal,9.Classify signals as energy type or power type,10.Know all the different definitions of bandwidth,11.Compute the bandwidth of a periodic signal,12.Classify signals as low-pass or band-pass,13.Define the Fourier transform and its inverse,14.

Sketch the amplitude spectrum and phase spectrum of a signal,15.Compute the Fourier transform of a signal by using the properties,16.Use the Fourier transform to compute the bandwidth,17.Use the Fourier transform to compute the energy.18.

Students should be able to

Essential learning outcomes - for Midterm 1Wednesday, January 29, 2014 8:42 AM

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Example: By using frequency-shifting and duality properties, find the FT of

ExampleThursday, January 23, 2014 6:50 PM

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Example: Sketch Find the Fourier transform.

ExampleThursday, January 23, 2014 6:50 PM

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Time-bandwidth product1. Distortion-free systems2.

Outline

Post lecture: these two topics were completed.


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Time-bandwidthFebruary 2, 2014 3:52 PM

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Example 1: Find RMS time duration.

Example 2: X(f)= tri(f). Find the RMS bandwidth.

Time-bandwidthMonday, February 03, 2014 9:13 AM

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Signal x(t) has an RMS duration of 0.1 seconds. Which of thefollowing can be its RMS bandwidth?

The RMS bandwidth of signal x(t)=() is

i-clickerMonday, February 03, 2014 10:28 AM

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Distortion refers to changing of the shape of the signal.

A transmission system is distortion free if Output is just a delayed version of input.

Distortion free systemsFebruary 2, 2014 4:18 PM

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Linear systems1. Low-pass filters2.

Outline


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Impulse response:

Frequency response:

Linear systemsThursday, January 23, 2014 6:50 PM

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The 3-dB bandwidth of a filter with response i-clickerWednesday, February 05, 2014 9:45 AM

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Quick reviewa.Example b.

Linear system -1.

Low-pass filters2.

Outline

Lecture #15Friday, February 07, 2014 9:54 AM

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Example: system impulse response is Find theamplitude and phase response.

ExampleFebruary 2, 2014 4:14 PM

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LTI system 3-dB

bandwidth

system The phase shift this system induces to input

signal is

•

i-ClickerFriday, February 07, 2014 10:32 AM

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Responsea.

Sinusoidal input b.Output energyc.Impulse responsed.

Low-pass filters1.

Introductiona.History b.

Amplitude modulation2.

Outline


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Definition:

Definition- using rectangular function

Input response and output response

Low-pass filter February 2, 2014 4:19 PM

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What happens when a pure sinusoidal signal is input to an ideal low-pass filter?

Sinusoidal inputsWednesday, February 05, 2014 9:24 AM

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If input signal is , what is the energy of the output signal?

Example: Signal with spectrum is input to a LPF of bandwidth 5

Hz. What is the output signal energy?

Output energyWednesday, February 05, 2014 9:24 AM

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What is the impulse response of the LPF

Impulse responseFebruary 2, 2014 4:19 PM

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Chapter 2 -SummarySunday, February 9, 2014 7:25 PM

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Outline

Introductiona.History b.Basic definitionsc.Double sidebandd.



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February 3, 2014

Double sideband-suppressed carrier (DSB-SC)1.Single sideband suppressed carrier (SSB-SC)2.Amplitude modulation3.

11:45 AM

Modulation

What is the best way to transmit

over wireless or wired channels?a.

What is the power required for transmission? b.What is the bandwidth required for transmission?c.What is the efficiency?d.What are the implementation methods?e.

What is the best way to recover by the receiving side?f.

Signal

is a message signal (voice, video)1.

Chapter 3 - Amplitude modulationSunday, February 9, 2014 5:20 PM

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History - ArmstrongSunday, February 9, 2014 6:32 PM

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message to be transmitted (voice, video) = modulating signal

= low-pass signal

= Bandwidth is

(Hz)

Modulation - using to generate a band-pass signal

Why modulation is necessary?

1. To match with the propagation characteristics of the channel

To realize wireless antennas.2.

What is modulation?Sunday, February 9, 2014 6:43 PM

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Scans = 30/second, 525 lines

Basic bandwidth = 4.2 MHz

Video signalsWednesday, February 12, 2014 10:02 AM

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One of the characteristic parameters of the radio signal, i.e., its amplitude, frequency, or phase is made to vary according to the time variation of the message. Typical examplesof modulation are radio and television broadcasting, sending digital data over the analogtelephone cable, etc.

Basic modulation conceptWednesday, February 12, 2014 10:18 AM

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Outline

Double sideband suppressed carriera.Single sideband suppressed carrier b.

c.


What we've got here is failure to

communicate.

Paul Newman in Cool Hand Luke


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Learning outcome: Students should be able to compute Bandwidth and Power and sketchthe amplitude and phase spectra.

Carrier signal:

DSB-SC signal is generated by multiplying the carrier signal by the message signal.

By substituting the carrier signal in this equation, we get

Using Euler's formula to represent the cosine signal, we get

Recall the frequency shifting property of the FT. That is, the FT of is

given by

- message signal -

for

DSB-SCWednesday, February 12, 2014 9:42 AM

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To compute the power, recall the definition of power of a signal

Power of DSB-SC signalThursday, February 13, 2014 8:28 PM

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Learning outcome: Students should be able to compute Bandwidth and Power and sketchthe amplitude and phase spectra.

DSB-SC signal - Because

is symmetric around

, frequency bands

And both carry the same information.

SSB-SC is obtained by filtering out one sideband of the DSB-SC signal.

SSB-SCWednesday, February 12, 2014 9:42 AM

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Outline

Reviewa.AM signal b.Bandwidthc.Powerd.



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Signals:

Message (modulating signal) -

- bandlimited to

Carrier signal -

DSB-SC SSB - LSB or USB of

Bandwidth

Power:

P_m(t)

P_m(t)

ReviewMonday, February 24, 2014 9:29 AM

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AM signal --

Modulation index1.Bandwidth requirements2.Efficiency3.Spectrum4.

Learning outcomes:

Basic signal definition

Amplitude ModulationSunday, February 9, 2014 7:19 PM

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Taking the FT of eq. 2, we find

FT(AM signal)= FT(Carrier) + FT(DSB signal)

Example: modulating signal

Determine the bandwidth and sketch the

spectrum.

Bandwidth requirementsMonday, February 24, 2014 9:51 AM

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Outline

Reviewa.Power b.


Demodulation2.


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AM- signal

DSB-SC signal

ReviewWednesday, February 26, 2014 10:30 AM

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Recall

Example: modulating signal and modulation index is 80%.Determine the power efficiency.

Efficiency of AM transmission

Note that the AM consists of carrier part and the DSB part. The message is embedded in DSB part. Thus the power spent on the carrier can be thought as an inefficiency. Thus, thratio of the DSB power to that of the total signal is called the transmission efficiency.

PowerMonday, February 24, 2014 10:13 AM

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Recovery of given the modulated signal (DSB, SSB or AM).

DSB-SC demodulation

Recall

Main idea (product demodulation)

Multiply by the carrier signal1.Filter out unnecessary parts2.

Note that the local carrier must be identical to the carrier signal generated by the

transmitter side. In practice, there are frequency shifts and phase shifts between the twocarriers.

This part is extractedBy an LPF.

This is the part located at twic

It should be filtered out.

DemodulationWednesday, February 26, 2014 9:19 AM

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Outline

Demodulation1.Envelope detection2.Superheterodyne receiver3.Quiz #44.


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AM demodulation

Recall

Main idea (product demodulation)

Multiply by the carrier signal1.Filter out unnecessary parts2.

DemodulationWednesday, February 26, 2014 9:19 AM

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Product demodulation requires exact copy of the carrier to be generated at the receivingside.

Input - positive - diode conducts and C charges. Input negative - Diode is open andC discharges through R.

If (1) is satisfied, the output of the RC circuit will track the envelope and can be recovered.

ken

Envelope detector (AM only)Wednesday, February 26, 2014 9:58 AM

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Thus, main idea is to down convert all incoming carrier frequencies to a constant frequencand perform the amplification at that frequency.Mixer - non-linear device that multiplies the two input signalsIF stage - constant frequency regardless of carrier frequency. This stage contains most of thamplification in the receiver as well as the filtering.

Multiple radio stations with different carrier frequencies must be handled by the RF AMPstage. This requires its gain to remain sufficient over this range. However, such widebandamps are more expensive and were not available during the early days of AM radio. z

Thus, both are possible carrier frequencies for a given pair of IF and local frequen

Superheterodyne receiverThursday, February 27, 2014 4:59 PM

Chapter 3

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