# Berkeley ELENG 120 - EE120 Midterm (3 pages)

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## EE120 Midterm

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Lecture Notes

- Pages:
- 3
- School:
- University of California, Berkeley
- Course:
- Eleng 120 - Signals and Systems

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EE120 Midterm 1 Spring 2004 Problem 1 Short Questions 20 Points For each of the following statements if you believe it is true give a justification If you believe it is false give a counterexample a A linear causal continuous time system is always time invariant b The system with real valued input x t and output given by y t 1 x t 2 cos t is stable c The discrete time signal x n cos n is a periodic signal d For an otherwise completely unknown system it is known that when the input is given by x t cos t cos 2t the output is y t 5 1 cos t cos 2t cos 3t This system cannot be a linear time invariant LTI system Problem 2 Convolution 20 Points The continuous time signals x t and y t are given in Figure 1 In the figure draw the signal z t given by z t x y t Carefully label both axes x t 1 1 1 t 1 y t 1 Figure 1 Convolution z t x y t Problem 1 Short Questions 20 Points 1 EE120 Midterm 1 Spring 2004 Problem 3 Inverse discrete time Fourier Transform 15 Points A discrete time signal h n has discrete time Fourier transform H e jw 1 e jw 1 5e jw Find the signal h n Problem 4 A linear time invariant system 30 Points A linear time invariant system with input x t and output y t satisfies a 2 y t 2a dy t dt d 2 y t dt 2 x t a 10 Points Find the frequency response H jw of the considered system b 10 Points For a 1 2 sketch the magnitude of the frequency response H jw Is the system rather high pass or rather low pass Justify your answer c 10 Points For what values of a is the system stable Justify your answer Remark If you cannot solve the math don t worry Just describe clearly and concisely how you would proceed and you will get partial credit Problem 5 Filtering 15 points The signal x t with spectrum X jw as shown in Figure 2 is passed through a linear time invariant LTI system with impulse response h t 2sinc 2t where as defined in class sinc t sin pi t pi t Denote the output fo the system by y t Calculate the error between x t and y t given by integral from infinity to infinity of x

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