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Midterm2c_2006

# Midterm2c_2006 - domain and frequency representations of...

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BME 513 Midterm #2 4/11/06 This test is closed notes, closed books. No calculators allowed. Show all work. Write your name on all pages NOW. Include your name on any extra pages you may require. A table of formulas is included. Some words of wisdom: Don’t just “dive” into the problem immediately. Take a few minutes to read the problem carefully. Draw some preliminary sketches of the signals can help immensely. Name________________________ I have neither given nor received aid in completion of this exam. Signature____________________________

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Name________________________ 1. Show that time integration of a function x(t) and convolution of x(t) with a unit step function u(t) are equivalent operations (15 points).
Name________________________ 2. Assuming that an LTI system has an impulse response h(t) = u(t), find the time

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Unformatted text preview: domain and frequency representations of the output when the input is (40 points): For inputs x 2 (t) and x 4 (t), sketch the magnitude of the Fourier transform of the output. Clearly label any pertinent values (10 points). ) ( ) ( ) ( ) ( ) 20 cos( ) ( ) 20 cos( ) ( ) ( ) ( 4 3 2 1 t t t t t x t u t t x t t x t u e t x t +--= = = =-δ π Name________________________ Name________________________ 3. What is an adequate sampling frequency for x 1 (t) in problem 2? Explain why you think this is an adequate sampling frequency. (10 points) Name________________________ 4. Sketch a sampled version of x 1 (t) in problem 2 and its corresponding discrete Fourier transform. Specify all pertinent values and their relationship between discrete time domain and discrete frequency domain. (25 points)...
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Midterm2c_2006 - domain and frequency representations of...

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