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HWchapter6solutions - Solutions to HW Problems from Chapter...

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Solutions to HW Problems from Chapter 6 Problem 6.2 Use the graphical method to convolve p P @ t A with p P @ t A . SOLUTION: The convolution duration property implies that p P @ t A p P @ t A a H for t P a I I and t P a I C I . For P t H , the convolution produces p P @ t A p P @ t A a IC t  I I d a t C P For H t P , the convolution produces p P @ t A p P @ t A a I  IC t I d a P t Problem 6.4 Use the graphical method to convolve triangularly shaped signals presented in FIGURE 6.29. f 1 (t) f (t) 2 0 1 1 t 0 1 2 1 t FIGURE 6.29 SOLUTION: By the convolution duration property, we have that f I @ t A f P @ t A a H for t H C I a I and t I C P a Q . In the time interval I t P , the convolution is given by f I @ t A f P @ t A a t I  H @ I C t A d a @ t IA Q Q C @ t IA P P @ t IA a I T @ t IA Q In the time interval P t Q , the convolution is given by f I @ t A f P @ t A a I  t P @ I C t A d a I Q C I P @ t IA C @ t PA Q Q @ t PA P P @ t IA 181
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CHAPTER 6 Problem 6.5 Convolve graphically the signals given in FIGURE 6.30. f 1 (t) f (t) 2 t 0 1 2 1 0 1 1 t FIGURE 6.30 SOLUTION: By the convolution duration property, we have that the convolution is equal to zero for t H C H a H and t I C P a Q . In the time interval
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