_Signal_Exam07AprQes - EE2009 Signals / page 1 NATIONAL...

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EE2009 Signals / page 1 NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION FOR (Semester II: 2006/2007) EE2009 – SIGNALS April 2007 – Time Allowed: 2 Hours INSTRUCTIONS TO CANDIDATES : 1. This paper contains SIX ( 6) questions and comprises NINETEEN (19) printed pages. 2. Answer any TWO ( 2 ) questions from Section A, and any TWO ( 2 ) questions from Section B. 3. All questions carry equal marks. 4. This is an OPEN BOOK examination. 5. Write your matriculation number and the numbers of the questions you have attempted in the spaces provided below. 6. All your answers must be written neatly in the appropriate spaces provided in the question paper. QUESTION NUMBER MARKS TOTAL MATRICULATION NUMBER :
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/ page 2 SECTION A (Answer Any TWO Questions) Q.1 (a) To synthesize a musical note from a certain instrument, an engineer contemplates using a signal of the form ( ) ( ) t j t f j 2 1 2 ω π () t x a f L + + + = a e a e a t t x 2 1 1000 cos 3 . In this summing equation for , and a are complex constants, and two terms are missing. Also, the signal is supposed to have a fundamental component plus a third and a fifth harmonics. Suggest a possible set of values for the constants and a 1 2 1 2 , and help the engineer to complete the series for ( ) t x a a a . What is the fundamental frequency of the musical note? Determine and sketch the amplitude and phase spectra of the signal as a function of frequency. In sketching the amplitude spectrum, use impulses. (15 Marks) (b) Depending on the choice of and , the musical note modeled by may produce a sound that comes from different instruments. However, regardless of the instrument being emulated, it is desired that the power of the sound should remain the same. Derive an equation that relates and such that this is fulfilled. In considering the power for 1 a 2 a () t x a 1 2 ( ) t x a , is the power an average value? Over what interval? Is the equation ( ) t x a for the musical note to be synthesized realistic? Give your answer to Q.1 in the space below. If necessary, continue on the next two pages.
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This note was uploaded on 08/02/2009 for the course ECE EE2009 taught by Professor Prof.c.c.ko during the Fall '07 term at National University of Singapore.

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_Signal_Exam07AprQes - EE2009 Signals / page 1 NATIONAL...

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