chapter one of system and signals course.pdf

this is chapter one with title of properties of signals

1. Signals and Systems –S&S
Arab International University (AIU)
Faculty of Informatics and Communication Engineering
Properties of signals
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2. Outlines
Properties of signals
Continuous-Time vs. Discrete-Time signals
Even –odd signals (symmetry)
Periodic –nonperiodic signals
Deterministic –random signals
Energy –power signals
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3. Continuous-Time vs. Discrete-Time Signals
Acontinuous-time(CT)signalisdefinedforall
valuesoftheindependentvariable??????.
Adiscrete-time(DT)signalisdefinedonlyatdiscrete
valuesoftime??????.
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4. Continuous-Time vs. Discrete-Time Signals
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5. Even signals
A CTsignal ??????
??????(??????)is said to be an evensignal if
??????
�(??????)=??????
�(−??????)
A DTsignal ??????
??????[??????]is said to be an evensignal if
??????
??????[??????]=????????????[−??????]
Geometrically,thegraphofanevensignalis
symmetricwithrespecttotheverticalaxis.
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6. Even signals
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7. Odd signals
A CTsignal ??????
o(??????)is said to be oddsignal if
??????
o(??????)=−??????
o(−??????)
A DTsignal ??????
o[??????] is said to be oddsignal if
??????
o[??????] = −??????
o[−??????]
Geometrically,thegraphofanoddsignalis
symmetricwithrespecttotheorigin.
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8. Odd signals
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9. Periodic CT Signals
•AperiodicCTsignal??????(??????)hasthepropertythatthere
isapositivevalueof??????forwhich
??????(??????)=??????(??????+??????)∀??????∈ℝ
•Aperiodicsignalisunchangedbyatimeshiftof??????.
•Wesaythat??????(??????)isperiodicwithperiod??????.
•Thefundamentalperiod??????
�isthesmallestvalueof??????.
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10. Periodic CT signal
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11. 11

12. 12
ECG is a Periodic CT signal

13. Periodic DT signal
A DT signal ??????[??????]is periodic with period ??????,
where ??????is a positive integer, if it is unchanged
by a time shift of ??????:
??????[??????]=??????[??????+??????]∀??????∈??????
The fundamental period ??????
�is the smallest
positive value of ??????
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14. Periodic DT signal
??????
�=�
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15. Deterministic -random signals
Anysignalthatcanbeuniquelydescribedbya
mathematicalexpression,atableofdata,orawell-
definedruleiscalleddeterministic.
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16. Deterministic –random signals
Signals that either cannot be described to any
reasonable degree of accuracy by mathematical
formulas, or such a description is too complicated
to be of any practical use, are random signals.
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17. Energy –power signals
The energyin the signal ??????(??????)is
??????=
−∞
∞
??????(??????)
�
�??????
The powerin the signal ??????(??????)is
??????=�??????�
??????→∞
�
�??????

−??????
??????
??????(??????)
�
�??????
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18. Energy –power signals
The energyin the signal ????????????is
??????=
−∞
+∞
??????[??????]
�
The powerin the signal ??????[??????]is
??????=�??????�
??????→∞
�
�??????+�

−??????
+??????
??????[??????]
�
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19. Power of periodic signals
The power in a periodic CTsignal of period ??????is
??????=
�
??????

−??????/�
??????/�
??????(??????)
�
�??????
The powerin a periodic DTsignal of period ??????is
??????=
�
??????

�
??????−�
??????[??????]
�
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20. Energy –power signals
Energy signal : if 0<??????<∞??????=0
Power signal : if 0<??????<∞??????=∞
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21. Energy –power signals
•An energy signal has zero time-averaged power,
whereas a power signal has infinite energy.
•Periodicsignals and randomsignals are
usually viewed as powersignals,
•Signals that are both deterministicand
nonperiodicare usually viewed as energy
signals.
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22. End of Lecture 1
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23. Requirements for Next Week
Revision of Complex Numbers
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