Homework2_ solutions

# F stable the system is bibo 211 for an ltic system an

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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: (i) 5x(t) (ii) 0.5x(t-1)+0.5x(t+1) (iii) x(t+1)-x(t-1) (i) (ii) (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) x[k]= [ −4 ] The response will...
View Full Document

## This document was uploaded on 03/06/2014 for the course EE 341 at NMT.

Ask a homework question - tutors are online