Dr. Prust. Assigned: 22 March 2013. Due: (will not be graded). 1. Consider the
system described by the difference equation y(n)=0.5x(n) - 0.3x(n - 2). (a) Identify
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EE3220-011 Homework 4 Dr. Prust Assigned: 22 March 2013 Due: (will not be graded)
1. Consider the system described by the difference equation y(n) = 0.5x(n) − 0.3x(n − 2) (a) Identify all coefficients ak and bk . (b) Is this a recursive filter or a non-recursive filter? Explain. 2. Consider a sequence x(n) = {1, 0, 3, 2, 1}. For each of the following systems, determine and plot the ↑
output of the filter. (a) y(n) = 0.5(x(n) + x(n − 1)) (b) y(n) = 0.6y(n − 1) + x(n) 3. Draw a block diagram for the system described by the following difference equation y(n) − 1.2y(n − 1) + 0.5y(n − 2) = 0.5x(n) − 0.1x(n − 1) 4. Consider the system described by the difference equation y(n) = x(n) − x(n − 1) Let the system input be x(n) = u(n) − u(n − 5). (a) Determine y(n). (b) Find the impulse response h(n) of the system. (c) Using convolution, determine y(n). Does your answer match part (a)? 5. Find the impulse response of the following systems. For each, state whether the system is FIR or IIR, and whether the system is causal or non-causal. (a) y(n) = 0.5x(n + 1) + x(n) − 0.3x(n − 1) (b) y(n) = −0.9y(n − 1) + x(n − 1)
