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Unformatted text preview: 11 For an LTIC system, an input x(t) produces an output y(t) as shown in Fig. P2.11.
Sketch the outputs for the following set of inputs:
(ii) 0.5x(t-1)+0.5x(t+1) (iii) x(t+1)-x(t-1) (i)
(iii) Using linearity property 5x(t) → 5y(t)
Using linearity property 0.5x(t-1)+ 0.5x(t+1) → 0.5y(t-1)+ 0.5y(t+1)
Using linearity property x(t-1)-x(t+1) → y(t-1)-y(t+1) 2.18 The output h[k] of a DT LTI system in response to a unit impulse function δ[k] is
shown in Fig. P2.18. Find the output for the following set of inputs: EE 341 Fall 2012 (i) x[k]=δ[k+1]+δ[k]+δ[k-1] (ii) x[k]= (iii) x[k]=u[k] (i) [ −4 ] x[k]=δ[k+1]+δ[k]+δ[k-1]
The impulse response is given by δ[k] → h[k]=δ[k+1]-2δ[k]+δ[k-1]
So the response to input x[k] is given by
δ[k+1] → h[k+1]=δ[k+2]-2δ[k+1]+δ[k]
δ[k] → h[k]=δ[k+1]-2δ[k]+δ[k-1]
δ[k-1] → h[k-1]=δ[k]-2δ[k-1]+δ[k-2]
So the total response is:
δ[k+1]-2δ[k]+δ[k-1] → δ[k+2]-δ[k+1]-δ[k-1]+ ]+δ[k-2] (ii)
[ −4 ]
The response will...
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This document was uploaded on 03/06/2014 for the course EE 341 at NMT.
- Fall '09