Lecture 38 - Lecture 38 Impulse response, convolution...

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Lecture 38 Impulse response, convolution
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Impulse response If have transfer function H(s) Then if inject an impulse, – Vin(t)= δ (t) – Vin(s)=1 – Vout(s)=H(s)Vin(s)=H(s) – Vout(t)=h(t) Impulse response = inverse Laplace of transfer function ( 29 ( 29 ( 29 RC t RC t h RC s RC s H - = + = exp 1 ) ( 1 1 V in (t) R C V out (t) Vin: Vout:
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Multi-impulse response • If have multiple impulses: – Each generates an impulse response – Responses superpose ( 29 ( 29 ( 29 RC t RC t h RC s RC s H - = + = exp 1 ) ( 1 1 V in (t) R C V out (t) 0 5 10 -1 -0.5 0 0.5 1 1.5 2 2.5 time Volts Vin Vout
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Multi-impulse response If have impulse train: Treat as sum of time-shifted impulses If pulses separated by t, height = t Each pulse generates as impulse response Also time shifted, superposed Include time shifted step function because response only starts at time pf impulse (this ensures causality) As t b 0, gets smoother Here approaches step response
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Lecture 38 - Lecture 38 Impulse response, convolution...

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