Linear system Lesson 3 Signals and systems Meiling

Linear system (1) Unit step function Shift a Meiling CHEN 2

Linear system (2) Unit impulse function Area=1 Amplitude width Meiling CHEN 3

Linear system (3) Unit doublet function Meiling CHEN 4

Linear system (4) sign function (5) Unit ramp signal Meiling CHEN 6

Linear system (6) parabolic signal (7) sinc signal Meiling CHEN 7

Linear system Signal Classification • • • Periodic and aperiodic Even and odd Real

Linear system Periodic signals Even signals odd signals Meiling CHEN 9

Linear system Causal signals Anticausal signals Meiling CHEN 10

Linear system Causal and noncausal system Example: distinguish between causal and noncausal systems in

Linear system (2) Case II Delay system causal system (3) Case III causal system

Linear system (4) Case IV noncausal system At present future (5) Case V noncausal

Linear system Signal operations • Simple operation : ＋、－ • Convolution : * Meiling

Linear system simple operation Meiling CHEN 15

Linear system Convolution Integral : Linear system Meiling CHEN … 16

Linear system I. C. =0 Impulse response Transfer function of the system Any input

Example : Graphical convolution Linear system (1) Meiling CHEN 18

Linear system Laplace and convolution integral Algebra operator Meiling CHEN 22

Laplace transform For causal signals pass through linear time-invariant causal systems Complex frequency f(t)

Laplace transform properties Meiling CHEN Linear system 26

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Linear system Lesson 3 Signals and systems Meiling CHEN

Linear system (1) Unit step function Shift a Meiling CHEN 2

Linear system (2) Unit impulse function Area=1 Amplitude width Meiling CHEN 3

Linear system (3) Unit doublet function Meiling CHEN 4

Linear system Sampling … Meiling CHEN 5

Linear system (4) sign function (5) Unit ramp signal Meiling CHEN 6

Linear system (6) parabolic signal (7) sinc signal Meiling CHEN 7

Linear system Signal Classification • • • Periodic and aperiodic Even and odd Real and complex Continuous-time and discrete-time Deterministic and stochastic (random) Causal and noncausal Meiling CHEN 8

Linear system Periodic signals Even signals odd signals Meiling CHEN 9

Linear system Causal signals Anticausal signals Meiling CHEN 10

Linear system Causal and noncausal system Example: distinguish between causal and noncausal systems in the following: (1) Case I Noncausal system Meiling CHEN 11

Linear system (2) Case II Delay system causal system (3) Case III causal system At present past Meiling CHEN 12

Linear system (4) Case IV noncausal system At present future (5) Case V noncausal system Meiling CHEN 13

Linear system Signal operations • Simple operation : ＋、－ • Convolution : * Meiling CHEN 14

Linear system simple operation Meiling CHEN 15

Linear system Convolution Integral : Linear system Meiling CHEN … 16

Linear system I. C. =0 Impulse response Transfer function of the system Any input Linear system I. C. =0 Meiling CHEN Zero state response 17

Example : Graphical convolution Linear system (1) Meiling CHEN 18

Linear system (2) (3) Meiling CHEN 19

Linear system (4) (5) Meiling CHEN 20

Linear system Ans: Meiling CHEN 21

Linear system Laplace and convolution integral Algebra operator Meiling CHEN 22

Linear system Example Meiling CHEN 23

Linear system Hint: Meiling CHEN 24

Laplace transform For causal signals pass through linear time-invariant causal systems Complex frequency f(t) F(s) 1 f(t) F(s) u(t) r(t) Meiling CHEN 25

Laplace transform properties Meiling CHEN Linear system 26