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 transcript:

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

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

1.System definition S xy

Examples: Time = R

Examples: Time = Ints

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

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

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

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

Time-invariance

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

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

Linearity

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

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

Frequency response of continuous-time LTI system

Calculating frequency response

v(t) i(t) y(t) R C LTI differential equations

Frequency response of discrete-time LTI system

Calculating frequency response

Difference equations