3 signal analysis - hawa.work signal analysis.pdflecture 3: review of signal analysis basics dr....

1/28/2018

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Lecture 3: Review of Signal Analysis Basics

Dr. Mohammed HawaElectrical Engineering Department

University of Jordan

EE421: Communications I

Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan

Exponential vs. Compact

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Exponential Fourier Series

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Single-Sided vs. Double-Sided

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Basic Signals

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Basic Signals

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Basic Signals

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Periodic SignalsrepT {A rect (t/ )}

t0

A

/2/2 TT 2T

repT {A (t/ )}

t0

A

TT 2T

repT {A saw (t/ )}

t0

A

/2 TT 2T

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Periodic SignalsrepT {2A rect (2t/T)} A

t0

A

TT 2T

repT {2A (2t/T)} A

t0

A

TT 2T

repT {A saw (t/T)}

t

A

2T

T/4T/4

A

A

T/4T/4

0

T/2

T/2

TT

A

T/2

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First-Null Bandwidth

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Fourier Transform

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Fourier Series vs. Tranform

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Periodic vs. Aperiodic

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DC vs. Average PowerThe DC value or average value of the signal �� is:

�� = �� = lim�→∞1��

� 2⁄

−� 2⁄

�� = �� = �0

The average power in the signal �� is:

�� = �2�� = lim�→∞1�� |��|2��

� 2⁄

−� 2⁄

�� = �2�� = 12��

∞

−∞

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DC vs. Average Power

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DC from Frequency Domain

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Power Spectral Density

PSD = �� = lim�→∞1� |��|2 = ℱ!"�� #�$

0

|Sx( )|

00

2 (A2/4)2 (A2/4)

0

|Sx( )|

00 00 0c

2 ( 02)

2 (c12/4)2 (c1

2/4)2 (c2

2/4)2 (c22/4)

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Quick Review of Filters

• There are three main filter types that you studied in signal analysis:

–LPF: Low-Pass Filter

–BPF: Band-Pass Filter

–HPF: High-Pass Filter

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Low-Pass Filter (LPF)

• Symbol:

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Frequency-response function

%�� = &'��&(��

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Characteristics

• Always centered at 0 rad/s.

• Bandwidth = Cut-off frequency = ω1 rad/s

• Gain = k.

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Example Circuit

)*�+ = 12�"� Hz

,-(. = 1

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Band-Pass Filter (BPF)

• Symbol:

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%�� = &'��&(��

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Characteristics

• Centered around center frequency ωc rad/s.

• Bandwidth of Filter = ω2 - ω1 rad/s

• Gain = k.

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Example Circuit

/0 = /123 = 12�√*� Hz

))�+ = ∆/ = "2�* Hz

,-(. = 1

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High-Pass Filter (HPF)

• Symbol:

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%�� = &'��&(��

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Characteristics

• Cut-off frequency = ω1 rad/s.

• Gain = k.

• No bandwidth defined.

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Example Circuit

/06�−'// = 12�"� Hz

,-(. = 1

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3 signal analysis - hawa.work signal analysis.pdflecture 3: review of signal analysis basics dr....

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