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exam2 - BME 311 Show all work in your blue book EXAM#2...

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BME 311 EXAM #2 March 29, 2006 Show all work in your blue book. Please start each problem on a new page, and clearly indicate your answers. Write and sign the honor pledge on the cover of your blue book: “I have neither given nor received unauthorized aid on this exam, nor have I concealed any violations of the Honor Code.” This test is closed-book and closed-note. Calculators are allowed. You may find these relations useful: x [ n ] = k = N X (e jkω 0 )e jkω 0 n c k = X (e jkω 0 ) = 1 N n = N x [ n ]e - jkω 0 n x ( t ) = k = -∞ X (e jkω 0 )e jkω 0 t c k = X (e jkω 0 ) = 1 T 0 T 0 x ( t )e - jkω 0 t d t x ( t ) = 1 2 π -∞ X ( )e jωt d ω X ( ) = -∞ x ( t )e - jωt d t ax 2 + bx + c = 0 has roots - b ± b 2 - 4 ac 2 a [ x - ( a + j b )][ x - ( a - j b )] = ( x - a ) 2 + b 2 1. [15] Find the Fourier spectrum for each of the following signals: (a) The periodic CT signal: ! 4 ! 2 0 2 4 0 0.5 1 1.5 x(t) t Signal where x ( t ) = e - t , 0 < t < 1 0 , 1 < t < 2 . (b) y ( t ) = e - t , 0 < t < 1 0 , otherwise 1
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BME 311 EXAM #2 March 29, 2006 (c) The periodic DT signal: ! 6 ! 4 ! 2 0 2 4 6 0 0.5 1 1.5 z[n] n Signal 2. [20] There are receptors in the airways of the lung that respond to the stretching of the airways’ walls.
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