ECE111_2007SPRING_EXAM2__[0]

ECE111_2007SPRING_EXAM2__[0] - The Cooper Union Department...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
The Cooper Union Department of Electrical Engineering ECEl11 Signal Processing & Systems Analysis Exam II April, Friday the 13'" 2007 Time: 2 hours. Closed book, closed notes. No calculators. SHOW ALL WORK!! L 14 pts.] A digital filter is given by, y(n) = 3x(n) - 2x(n-l) +5x(n- 2) +6x(n - 3) Specify the impulse response, transfer function and frequency response of the filter. Sketch a transversal filter realization. Is the filter FIR or 1IR? 2. [4 pts.) Sketch a direct fonn II transposed realization of: ,I H (z) = 2z' + 5z + 4 4z 2 - z+2 3. [6 pt's.] Use the method of partial fractions to find the inverse Laplace transform of: 2s 2 +s+1 H (5) = (5 + 5) (5 H) 4. [6 ptis.) Use the method. of partial fractions to find the inverse z-transfonn of: Hz _ z2+ z +1 ( ) - (2z - 1) (3z + 2) 5. [6 ptls.] The unit step response of a stable analog system is: Y (t) = 5u (t) + [4t 3 - t + 7J .-"u(t) + te-' cos (3t) u (t) - e-' sin (3t) u (t) , (a) Specify the term or terms associated that comprise the forced response. I (b) he remaining terms are denoted the response. (c) Specify the system poles, with multiplicity. [ (d) If we wanted to approximate this system with a second order model, should we J se:~e:~d:~~:~:~ :e~:l~:~ ,?~~:iticallY damped system? m~:~i~f ~~: I ----------- transient response does (does not) exhibit " 1 . t
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6. [9 pts.] Recall that, for a discrete-time system, the time-con.stant (in seconds) asso- ciated with a mode with pole p is given by: T T~-- lin Ipll where T is the sample period. A real discrete-time system is operated at a sampling rate Is = 1MH z. The system is represented in state-space form as {A, B, C, D}, and the associated transfer function matrix is H (z). The eigenvalues of A are: simple at -2, simple -1/3 ± j1/3 and triple multiplicity at +0.20. (a) The system is not internally stable. Why not? Be BRIEF. (b) Suppose H (z) is a stable transfer function for this system. What could be the poles of H?
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/27/2012 for the course CHEMISTRY/ CH/ECE/PH/ taught by Professor Faculty during the Spring '08 term at Cooper Union.

Page1 / 5

ECE111_2007SPRING_EXAM2__[0] - The Cooper Union Department...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online