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Homework 1

Homework 1. Problem 2.4. Given: Find y[n] y[0]=0, y[1]=2, y[2]=3/2, y[3]=7/8, y[4]=15/32. Problem 2.15. u [n]. h [n]. w [n ]. X[n]. y[n ]. System LTI?, Causal?, BIBO?. Problem 2.15. For LTI, test : Let then But. Problem 2.15. Causal? From LTI test: , For n=0

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Homework 1

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  1. Homework 1

  2. Problem 2.4 • Given: Find y[n] y[0]=0, y[1]=2, y[2]=3/2, y[3]=7/8, y[4]=15/32

  3. Problem 2.15 u[n] h[n] w[n] X[n] y[n] System LTI?, Causal?, BIBO?

  4. Problem 2.15 • For LTI, test: Let then But

  5. Problem 2.15 • Causal? From LTI test: , For n=0 Not Causal

  6. Problem 2.15 • BIBO? • Since h[n] is bounded and multiplying by u[n] will not cause it to become unbounded it is stable

  7. Problem 2.20 • Consider the following Causal LTI system: • Find impulse response, h[n] (b) Range of values for a? a>1

  8. Problem 2.21 • Given a sequence, x[n]: • (a) Sketch x[n-2]: • (b) Sketch x[4-n]: • (c) Sketch x[2n]: • (d) Sketch x[n]u[2-n]: • (e) Sketch x[n-1]

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