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Dubai

Presentation On SIGNALS AND SYSTEM

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Published in: Science
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This ppt explains about 1.classification of signals 2.basic signals operation 3.causal and non causal system 4.convolution 5.laplace transform

Aswathi K / Abu Dhabi

4 years of teaching experience

Qualification: Bachelor of Engineering in AE&I

Teaches: Electronics, Physics, Engineering, Electrical Technology, Biology, Social Studies, Maths, Chemistry, Mathematics

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  1. Linear system Lesson 3 Signals and systems
  2. (1) Unit step function 1, u(t) Shift a u(t — a) 1 1 a Meiling CHEN Linear system 2
  3. (2) Unit impulse function ö(t) = lim —[u(t) — u(t — a)] ö(t) (1) 1 a Amplitude width 0 dt kö(t — a) (k) a Meiling CHEN Linear system Area= 1 3
  4. (3) Unit doublet function (1) Meiling CHEN Linear system 4
  5. Linear system Sampling Meiling CHEN 5
  6. (4) sign function sgn( t) (5) Unit ramp signal t, r(t) l, r(t) dr(t) u(t) dt r(t) = f Meiling CHEN Linear system 6
  7. (6) parabolic signal 2 (7) sinc signal sin m sin c(t) Meiling CHEN Linear system 7
  8. 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 Linear system 8
  9. Periodic signals f (t) = Even signals odd signals Meiling CHEN Linear system 9
  10. Causal signals f (t) = 0, for all Anticausal signals f (t) 0, for all Meiling CHEN Linear system 10
  11. Linear system Causal and noncausal system Example: distinguish between causal and noncausal systems in the following: u(t) -1 (1) Casel y(t) = u(-t) Y(t) 2 when but u(t) -2 1 Noncausal system Meiling CHEN
  12. (2) Case 11 y(t) — u(t -T) Y(t) —I—T (3) Case 111 Y(t) 2—T — Ll(t) + Ll(t past -2) At present Meiling CHEN Linear system Delay system causal system causal system 12
  13. (4) Case IV At present (5) Case V Linear system noncausal system future y(t) = Y(t) Meiling CHEN u(t) is unit when t 0 but y (t) O step u(t) = 0 noncausal system 13
  14. Signal operations Simple operation : + Convolution : * Meiling CHEN Linear system 14
  15. simple operation f(t) u(t) — u(t) — r(t) + — 1) r(t — 1) r(t) Meiling CHEN Linear system 15
  16. Linear system g(t) —T)dT Convolution Integral : Linear system u(t) Linear system Meiling CHEN h(t) u(t) * h(t) 16
  17. ö(t) = El(s) Any input Linear system l.c.-o Linear system (t) Impulse response Transfer function of the system Linear system l.c.-o Zero state response f (t) * h(t) 17 Meiling CHEN
  18. Example : Graphical convolution h(t) -2 h(t — T) u(t) -2 3 =4-t/2 8 Y(t) u(T) 3 Meiling CHEN Linear system 18
  19. (2) h(t — T) —2t (3) -2 h(t — T) u(T) u(T) 3 Meiling CHEN Linear system ---—)dT 2 ---—)dT 2 19
  20. (4) -2 (5) -2 u(T) 11 t u(T) h(t Y(t) 3 3 h(t Meiling CHEN Linear system -—)dT 2 Y(t) 20
  21. Ans.' 11 -K t Y(t) Y(t) Y'(t) =ft3 Y(t) Y(t) Meiling CHEN ---—)dT 2 ——)dT 2 --—)dT 2 Linear system 21
  22. Laplace and convolution u(t) Y(t) h(t) Il(s) Meiling CHEN Linear system — u(t) * h(t) integral Algebra operator 22
  23. Example =4-t/2 -2 u(t) 3 h(t) h'(t) ô(t) 4 8 h"(t) = ô'(t) 1 1 Linear system 8 LI'(t) = ô (t + 2) — ô (t —3) 8 —sh(0 ) 2 2s Meiling CHEN 23
  24. (2s -1) 3 2s Hint: L[f(t — — T)] = e Meiling CHEN Linear system 24
  25. Laplace tran#orm For causal signals pass through linear time-invariant causal systems X (s) = L{x(t)} = fo x(t)e stdt f(t) ö(t) u(t) r(t) 2 1 1 1 2 1 3 where s = c + jo Complex frequency f(t) u(t) sin oot u(t) cos oot —at 00 S +00 1 (s+a) Meiling CHEN 25
  26. Laplace tran#orm properties + ßg(t)] = aF(s) + PG(s) L[f(t — T)u(t — T)] = sF(s) - = snF(s) - sn If(0 e ßf(s) ) —sn 2 f '(0 UFO) dsn Meiling CHEN Linear system - dF(s) ds 26

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