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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 response
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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1.System definition S xy
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Examples: Time = R
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Examples: Time = Ints
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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S x w t S(x) t S(w)
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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Time-invariance
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0 -T-T 0 0 -T-T 0 00
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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Linearity
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Examples: The following systems are linear (L) and/or time-invariant (TI)
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1.System definition 2.Memoryless systems 3.Causal systems 4.Time-invariant systems 5.Linear systems 6.Frequency response
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Frequency response of continuous-time LTI system
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Calculating frequency response
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v(t) i(t) y(t) R C LTI differential equations + + - -
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Frequency response of discrete-time LTI system
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Calculating frequency response
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Difference equations
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