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# Homework_5 - 1 EE113 Homework 5 Problem 6.7 Evaluate the...

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1 EE113 Homework 5 Problem 6.7 Evaluate the convolution sum u ( - n +2) parenleftbigg 1 3 parenrightbigg n - 1 · u ( n - 2) using both the analytical and graphical methods. Compare your results. Problem 6.9 Evaluate parenleftbigg 1 2 parenrightbigg n - 1 · u ( n ) bracketleftbiggparenleftbigg 1 3 parenrightbigg n · u ( n - 2) - u ( n +1) bracketrightbigg using the distributivity property of the convolution sum. Problem 6.23 Consider two possibly complex-valued sequences x ( n ) and h ( n ) . Their cross-correlation is the sequence r xh ( n ) whose samples are defined as follows: r xh ( n )= summationdisplay k = -∞ x ( k ) h * ( k - n ) (a) Verify that r xh ( n )= x ( n ) ⋆h * ( - n ) . (b) Use the graphical method to evaluate the correlation of the two sequences: x ( n )= {- 2 , 1 , - 1 , 2 } and h ( n )= { 0 , 1 , 2 } Problem 6.31 A causal LTI system is described by the difference equation y ( n )= 1 4 y ( n - 1)+ x ( n - 1) Find its impulse response sequence. Find also the response to the input sequence shown in Fig. 6.18 using the convolution sum method. Problem 7.9 Determine the solution of each of the following homogeneous equations with initial conditions:

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Homework_5 - 1 EE113 Homework 5 Problem 6.7 Evaluate the...

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