ECE NAME: Please do NOT write your name on any pages after this one. 4 LISTED HERE WILL BE: (a) THE NUMBER OF QUESTIONS TO BE ATTEMPTED (b) POINT VALUE OF EACH QUESTION 2 Closed book TI89/HP48 calculators allowed, but you must show all work 9 Included tables: z-Transform pairs z-Transform properties Trig identities Geezer PLEASE REMEMBER THIS CLASS ID NUMBER (IT WILL BE USED FOR MAILING YOUR SCORES):
ECE 429 Exam 1 PART A Multiple choice questions: You may circle more than one answer. For a given question a point will be awarded only if ALL correct answers (and no incorrect ones) are circled. 1. The equation of the following discrete-time sequence is: (a) x(n) =(-1)" (b) x(n)= (1)n +1 (c) x(n)= (-1)"+1 2. The ROC of the z-transform of the sequence u(n+4) is: (a) |z| < 00 (b) 1 <|z| < 00 (c) |z| > 1 1. n=0 n .- 1 3. The sequence x(n) = 3 sin(0.5mn) was created by sampling a continuous sinusoid at a sampling rate of 18 kHz. What was the frequency (in Hz) of the continuous sinusoid, assuming no aliasing? (a) 4500 Hz (b) 9 kHz (c) 2250 Hz 4. What is the order of this LTI system? (a) first order (b) second order (c) third order (d) higher than third order x(n) -1 Z 0.25 0.25 Z Z -1 -1 0.25 0.25 -y(n) 5. Given are the transfer function and ROC of LTI systems. Which systems are unstable? 1+2z-1 (a) H(z)= 1+3z-1 (b) H(z) = 1+2z-1 1+0.8z? (c) H(z)= 1+z-1 1+2.5z +7 2 (d) H(z) = 107-4 1+0.6z 1 (e) All are stable. | z| <3 | z| > 0.8 0.5<|z|<2 | z| < 0.6 2
ECE 429 Exam 1 6. The region-of-convergence of the z-transform of the sequence x(n)= - (-1)" u(n-2)+(4)" u(-n+1) is: (a) | z|4 (c) ?Az|<4 (d) 0 <| z |< 4 7. All causal LTI FIR filters have all of their poles at z=0. (a) true (b) false 8. The impulse response of the digital filter y(n) = ax(n-2)+by(n-1) is: (a) h(n) =a 2(b)"-2u(n-2) (b) h(n)= a(b)" u(n) (c) h(n) = a(b) " 2u(n) (d) h(n)= a(b)"2 u(n-2) 9. The z-transform of the sequence: x(n) = 2" u(-n) is: -1 (a) X(z)= 1+2z-1 1 |z|<2 (b) X(z) = 1-0.5z 1 (c) X(z)= 1+0.5z? | z|> 0.5 |z|<2 10. The result of the convolution: {-1 2 -1} * u(n) can be written as: (a)-Ă²(n) + 8(n-1) (b)-(n) + 28(n-1) -8(n-2) (c) -6(n) + 28(n-1) (d) (n) 3 (b) ?<zk8