Problem1. The input x[n] and the output y[n] of a system are related by the equation y[n]=x[n-1]+x[1-n]. Is the system time invariant (yes/no)? Justify your answer. Solution. No: x[n]→ [time delay n0] →y[n]=x[n-n0] → [system] →z[n]=y[n-1]+y[1-n] =x[n-n0-1]+x[1-n-n0]=x[(n-1)- n0]+x[(1-n)-n0] x[n]→[system] →y[n]=x[n-1]+x[1-n] →[time delay n0] →z[n]=y[n-n0]= x[n-n0-1]+x[1-(n-n0)]=x[(n-1)- n0]+x[(1-n)+n0] Problem2. (from book 1.27) In this chapter, we introduced a number of general properties of systems. In practular, a system may or may not be a)memoryless b)Time invariant 3)linear 4)causal 5)stable Determine which of these properties hold and which do not hold for each of the following continuous- time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input. a)y(t)=x(t-2)+x(2-t) b)y(t)=cos(3t)x(t) c) Solution.
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y[n]=x[n ] → [system] → x[n]→[system] →y[n]=x[n n] →[time ...comp.eng.ankara.edu.tr/files/2013/03/COM336Problems.pdf · The input x[n] and the output y[n] of a system are
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Problem1. The input x[n] and the output y[n] of a system are related by the equation
y[n]=x[n-1]+x[1-n].
Is the system time invariant (yes/no)? Justify your answer.