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Lec_A1

# Lec_A1 - EE 303 EE Signals and Signals Transform Methods...

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EE 303 EE 303 Signals and Signals and Transform Methods Transform Methods EE 303 1

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Lecture 1 Basic Continuous-Time Signals EE 303 2
EE 303 3

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EE 303 4
EE 303 5

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CT Signals: Rectangular Pulse EE 303 6 ± Centered rectangular (square) pulse with time duration ± General rectangular pulse centered at ) ( ) 2 ( ) 2 ( ) ( τ t t u t u t p Π + = ) ( ) 2 ( ) 2 ( ) ( 0 0 0 t t t t u t t u t p Π = + = 0 t
) ( τ t Π t 2 2 ) ( 0 t t Π t 2 0 t 2 0 + t 0 t EE 303 7

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() [ ] ) 3 ( ) ( cos ) ( + = t u t u t t x θ ω EE 303 8
EE 303 9

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EE 303 10
EE 303 11

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EE 303 12
EE 303 13

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Energy Signals EE 303 14 ± Signal is an energy signal if ± Example: One-sided exponential signal ) ( t x < = dt t x x E ) ( 2 ) ( ) exp( ) ( t u t t x α = 2 1 0 | 2 ) 2 exp( 0 ) 2 exp( = = = t dt t x E
Power Signals ± Energy of power signals is infinite ± Average power over an interval is ± Periodic signals are power signals = 2 1 ) ( 2 1 2 1 T T dt t x T T x P EE 303 15

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Lecture 2 Linear Transformation of Time EE 303 16
Time Transformation: 1. Shifting (Delay) EE 303 ± Time-shifted transform of signal by time constant is ± Example: One-sided exponential signal ) ( ) ( 0 t t x t y = ) ( t x 0 t ) ( ) exp( ) ( t u t t x α = ) ( )] ( exp[ ) ( 0 0 t t u t t t y = 17

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EE 303 18
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Lec_A1 - EE 303 EE Signals and Signals Transform Methods...

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