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EELE445 Exam 1 ReviewIn class Friday March 20

50 minutes

• One 8x11page, both sides• 10 questions, 10 points per question,divided among 5 problems

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Exam 1 EELE445The exam covers through lecture 16and through homework 4.

• Be sure to review and understand the Homeworkproblems. The exam questions center on thematerial covered by the homework.

•Review the example problems worked in class

•Concepts highlighted in green or blue on theslides.

The following slides are indicative of theareas that will be covered on the exam,BUT ARE NOT ALL INCLUSIVE! You areresponsible for the material in the lectures

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TOPICS

• Review of Signals and Spectra• Analysis and Transmission of Signals• Sampling and pulse code modulation• Principles of Digital Baseband Signals• Bandpass Signaling Principles and Circuits• Bandpass Modulated Systems• Introduction to the theory of probability• Analog systems in the presence of noise• Behavior of digital systems in the presence of noise• Error correcting codes• Example systems

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TOPICS• Review of Signals and Spectra and information

– Shannon’s Channel Capacity Law– LOS tower height– DC, rms, power in time domain– voltage spectra, power spectra , PSD , Fourier series and Fourier transforms– continuous and discreet spectra– power in frequency domain

• Analysis and Transmission of Signals– dBm, dBW, dBV,– noise or equivalent bandwidth– lowpass and bandpass filters- Butterworth filter- 1 pole Beq=B3dBxp/2– be able to calculate the power of white noise through a filter– waveform through a transfer function, output spectrum and output power for a given input

spectrum– total power from a PSD

• Sampling and pulse code modulation– impulse, natural, and flat top sampling- what are the spectrum differences– Sample rate– sampled signal in frequency domain- spectra

• Principles of Digital Baseband Signals– PAM, PCM– PCM- bit rate, SQNR vs n-bits– m-law compression– line code spectra will not be covered this exam

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Lecture 1-2 – LOS Line of Sight

hd 2=d in miles, h in feet

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Lecture 1-2 – Shannon’s Law

sbitsNSBC

CapacityChannel

sbitsTHR

/1log

:

/

2 ÷øö

çèæ +·=

=

wattsinpowerNoiseNwattsinpowerSignalS

HzinBandwithB

===

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Lecture 1-2 – Units and dB

2161

211

22

2

1

21

2

1

10log20

1log20

1log10

1log10

001.0log10

log10log10

RRwhenrmsvoltrmsvoltsinVVdB

RRwhenrmsvolt

rmsvoltsinVdBV

wattwattsinPdBW

milliwattmilliwattsinP

wattwattsinPdBm

VR

RV

PPdB

rms

rms

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-m

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Lecture 3-4 – DC,rms, Power, Energy

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2

twofmeanorCDdttwT

tw

T

T

== ò-

)()(1)(2

2

22 twofvaluermsdttwT

tw

T

T

== ò-

òò--

==2

2

22

2

2 )()(1T

T

T

T

dttiRdttvR

E

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Lecture 5-7 – Frequency Domain

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Lecture 5-7

11

Lecture 5-7

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Fourier Series from Fourier Transforms

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Fourier Series from Fourier Transforms

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Fourier Series from Fourier Transforms

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Fourier Series from Fourier Transforms

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Lecture 8-10 – Power Through a Filter

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nny òå

¥

¥-

¥

-¥=

=÷÷ø

öççè

æ= 22

2

0

2

)()(

Be able to calculate the noise power at theoutput of a RC filter with a white noise input

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Natural Sampling

Duty cycle =1/3

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Natural Sampling

ss f

df 3=atNull

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Lecture 11-13 companding

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Lecture 11-13 Companding

U=255 U.S

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Lecture 11-13 Quantization noise

( ) noiseonquantizatithePM

V

dqqq

nq==

D=

D= ò

D

D-

2

2max

2

2

2

22

3

12

1

22

SQNR - summary

powernoiseonquantizatiM

VPnq 2

2max

3=

2max

2max

2 433V

PV

PMPPSQNR x

nx

nq

x ´===

• M is the number of quantization levels• n is the number of bits• Vmax is ½ the A/D input range

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SQNRdB

12max

2max

£

£

VP

VP

x

x The SQNR decreases asThe input dynamic rangeincreases

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10 ++÷÷ø

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æ@ n

VPSQNR x

dB

rangequantizerscalefulltheinbitsofnumbertheis

quantizertheofrangepeaktopeakthe2

is

n

V

·

·1

max

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Lecture 14-15 SQNR

( )[ ]

[ ]

quantizertheoflevelvoltagedesignpeaktheispowersignalinputtheis

26c)-(3)compandinglaw-(

26b)-(3)compandinglaw-(

26a)-(3)quantizing(uniform

25)-(3

max

2

max

ln1log2077.4

1lnlog2077.4

log2077.4

02.6

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AA

xV

nSQNR

xrmsx

xrms

dB

=

+-@

+-@

÷÷ø

öççè

æ-=

+=

a

mma

a

a

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Exam 1 EELE445

•Review the slides for lectures up to and including L16•concentrate on highlighted information•HW solutions 1-4