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final-exam - EECS 20n: Structure and Interpretation of...

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EECS 20n: Structure and Interpretation of Signals and Systems Department of Electrical Engineering and Computer Sciences U NIVERSITY OF C ALIFORNIA B ERKELEY Final Exam 14 May 2005 LAST Name FIRST Name Lab Time Please write you name and Lab Time in the spaces provided above. This exam consists of a total of 20 pages, including a double-sided appendix sheet containing transform properties. When you are permitted to begin work, verify that your copy contains all the pages and that there are no print- ing anomalies. If you detect a problem, please notify the staff immediately. The exam should take you up to 3 hours to complete. We recommend that you budget your time according to the point allocation for each problem and/or part thereof. Please limit your work to the space provided for each problem. No other work will be considered in grading your exam. Please write neatly and legibly, because if we can’t read it, we can’t grade it. Full credit will be given only if your work is clearly explained. Problem Points Your Score 1 5 2 15 3 10 4 15 5 25 6 15 7 20 8 10 9 15 Total 130 1
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Complex exponential Fourier series synthesis and analysis equations for a periodic discrete-time signal having period p : x ( n ) = X k = h p i X k e ikω 0 n ←→ X k = 1 p X n = h p i x ( n ) e - ikω 0 n , where p = 2 π ω 0 and h p i denotes a suitable contiguous discrete interval of length p (for example, X k = h p i can denote p - 1 X k =0 ). Complex exponential Fourier series synthesis and analysis equations for a periodic continuous-time signal having period p : x ( t ) = X k = -∞ X k e ikω 0 t ←→ X k = 1 p Z h p i x ( t ) e - ikω 0 t dt , where p = 2 π ω 0 and h p i denotes a suitable continuous interval of length p (for example, Z h p i can denote Z p 0 ). Discrete-time Fourier transform (DTFT) synthesis and analysis equations for a discrete-time signal: x ( n ) = 1 2 π Z h 2 π i X ( ω ) e iωn ←→ X ( ω ) = X n = -∞ x ( n ) e - iωn , where h 2 π i denotes a suitable continuous interval of length 2 π (for example, Z h 2 π i can denote Z 2 π 0 or Z π - π ). Continuous-time Fourier transform (CTFT) synthesis and analysis equations for a continuous-time signal: x ( t ) = 1 2 π Z -∞ X ( ω ) e iωt ←→ X ( ω ) = Z -∞ x ( t ) e - iωt dt . 2
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Problem 1 (5 Points Total) A causal system is initially at rest (i.e., all initial con- ditions are zero) and is described by the following delay-adder-gain block diagram. The block D denotes a delay by one sample; that is, if the input to the delay block D is a signal p
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final-exam - EECS 20n: Structure and Interpretation of...

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