Lecture 36_v2

# Lecture 36_v2 - Spring 2011 ECE 2100 Cornell Univ Prof...

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Unformatted text preview: Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 1 Lecture 36 Impulse response, convolution Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 2 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: Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 3 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) 5 10-1-0.5 0.5 1 1.5 2 2.5 tim e Volts Vin Vout Spring 2011 ECE 2100, Cornell Univ, Prof. Molnar 4 Multi-impulse response • If have impulse train: – Treat as sum of time-shifted impulses – If pulses separated by ∆ t, height = ∆ t • Each pulse generates an impulse response – Also time shifted, superposed...
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Lecture 36_v2 - Spring 2011 ECE 2100 Cornell Univ Prof...

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