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ece 313 hw 5 - x n h n and y n(b Repeat part(a for input...

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ECE 313 - Homework 5 Practice Problems: Not Due for Credit DT Impulse Response and Convolution 1. Roberts; Chapter 7, Problem 2. 2. Roberts; Chapter 7, Problem 3. 3. Consider a DT LTI system with impulse response h [ n ] = 1 , 3 4 , 1 2 , 1 4 for n = 0 , 1 , 2 , 3 . (a) Obtain the response y [ n ] of this system to the input x [ n ] = 3 δ [ n ] . (b) Obtain the response y [ n ] of this system to the input x [ n ] = - 2 δ [ n - 1] . (c) Obtain the response y [ n ] of this system to the input x [ n ] = δ [ n - 3] . Your answers should be in the form of graphs for each signal. 4. Obtain the response y [ n ] of the system of Problem 2 to the input x [ n ] = 3 δ [ n ] - 2 δ [ n - 1] + δ [ n - 3] .
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5. Consider a DT system with impulse response h [ n ] = w [ n ] 1 2 n with w [ n ] = u [ n ] - u [ n - 3] . (a) Obtain the response y [ n ] of this system to the input signal x [ n ] = u [ n ] - u [ n - 4] . Your answer should include graphs of
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Unformatted text preview: x [ n ], h [ n ], and y [ n ]. (b) Repeat part (a) for input signal x [ n ] = u [ n ]-2 u [ n-2] + u [ n-4] . Your answer should be in the form of a graph of y [ n ]. 6. The output y [ n ] resulting from input x [ n ] to a DT LTI system with impulse response h [ n ] is, of course, given by the convolution sum y [ n ] = x [ n ] * h [ n ] . For a DT system with impulse response h [ n ] = 2 δ [ n ] + δ [ n-1] and “truncated ramp” input x [ n ] = { 1 , 2 , 3 } for n = 1 , 2 , 3 , obtain y [ n ] by evaluation of the convolution sum using both • the “additive” graphical evaluation. • the “multiplicative” graphical evaluation. 2...
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