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Week 8 Linear time-invariant systems, Ch 8 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency.

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Presentation on theme: "Week 8 Linear time-invariant systems, Ch 8 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency."— Presentation transcript:

1 Week 8 Linear time-invariant systems, Ch 8 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

2 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

3 1.System definition S xy

4 Examples: Time = R

5

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7 Examples: Time = Ints

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10 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

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12 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

13 S x w t S(x) t S(w)

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15 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

16 Time-invariance

17 0 -T-T 0 0 -T-T 0 00

18 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

19 Linearity

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21 Examples: The following systems are linear (L) and/or time-invariant (TI)

22 1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response

23 Frequency response of continuous-time LTI system

24 Calculating frequency response

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27 v(t) i(t) y(t) R C LTI differential equations + + - -

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30 Frequency response of discrete-time LTI system

31 Calculating frequency response

32 Difference equations

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