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Unformatted text preview: ECE 301 Division 2 Exam 2 Solutions, 10/27/2010, 89:45pm in EE170. • Your ID will be checked during the exam. • Please bring a No. 2 pencil to fill out the answer sheet. • This is a closedbook exam. No calculators are allowed. – Instructor: Ilya Pollak – Course: ECE 301 – Date: 10/27/2010 – Test: 2 – sign the answer sheet – fill in your last name and the first six letters of your first name – fill in your student ID – for the section, fill in “0002” • You have 1 hour 45 minutes to complete 25 multiplechoice questions. • Each correct answer is worth two points, for a total of 50 points. • Please only turn in the answer sheets. 1 Some Formulas DT Fourier series for an Nperiodic signal x : x [ n ] = 1 N N 1 X k =0 a k e j 2 πkn N , where a k = N 1 X n =0 x [ n ] e j 2 πkn N , for k = 0 ,...,N 1 . Decomposition in an orthogonal basis: for any Mdimensional vector space G with orthogonal basis { g 1 ,..., g M } , and for any vector g ∈ G , g = M X k =1 a k g k , where a k = h g , g k i h g k , g k i , for k = 1 ,...,M. 2 Question 1. The response of a DT system S 1 to any input signal is the convolution of the input signal with signal h 1 , where h 1 [ n ] = δ [ n + 1] + 2 δ [ n ] + 3 δ [ n 1] for all integer n . Select the correct statement: 1. System S 1 is causal and BIBO stable. 2. System S 1 is not causal and is BIBO stable. 3. System S 1 is causal and is not BIBO stable. 4. System S 1 is not causal and is not BIBO stable. 5. System S 1 is BIBO stable, but it cannot be determined whether or not it is causal based on the given information. 6. System S 1 is not BIBO stable, but it cannot be determined whether or not it is causal based on the given information. 7. System S 1 is causal, but it cannot be determined whether or not it is BIBO stable based on the given information. 8. System S 1 is not causal, but it cannot be determined whether or not it is BIBO stable based on the given information. 9. Based on the given information, it cannot be determined whether or not S 1 is causal, and it cannot be determined whether or not it is BIBO stable. Solution. The system satisfies the convolution relationship. Since its impulse response is absolutely summable, it is BIBO stable. Since its impulse response is nonzero for n = 1, it is noncausal. The correct answer key is therefore 2. 3 Question 2. The response of a DT system S 2 to any input signal is the convolution of the input signal with signal h 2 , where h 2 [ n ] = δ [ n ] + δ [ n 2] for all integer n . Select the correct statement: 1. System S 2 is causal and BIBO stable. 2. System S 2 is not causal and is BIBO stable. 3. System S 2 is causal and is not BIBO stable....
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 Fall '06
 V."Ragu"Balakrishnan
 Digital Signal Processing, LTI system theory, system S, BIBO

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