Hwk6f06 - (d Determine the ±ourier TransForm oF y t(e...

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ECE 3337 Homework 6 Fall 2006 Due: November 20 (Jansen), 21 (Kalatsky) 2006 1. Sampling problem: (a) A telephone conversation is to be sampled. Typically, telephone conversations are low-passed flter with a cut-oﬀ at 3.5 KHz. What should be the minimum sampling rate? (b) A wireless telephone conversation is to be sampled. The same lowpass fltering is applied, but this time the conversation is modulated to 1.5 GHz. What should be the minimum sampling rate? 2. A system has impulse response h ( t ) = exp - 0 . 5 t u ( t ) , and produces ouput y ( t ) = 2(exp - t - exp - 0 . 5 t ) (a) Discuss whether the system is low-pass, high-pass or band-pass. (b) Is the system stable? (c) Determine the Frequency response oF the system.
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Unformatted text preview: (d) Determine the ±ourier TransForm oF y ( t ). (e) Determine x ( t ) by applying the convolution property and inverse ±ourier TransFormation. 3. ±ind the signal For which the ±ourier TransForm is: (a) X ( ω ) = 2 jω + 10 jω ( jω + 10) (b) Suppose x ( t ) is modulated with m ( t ) = sin( ω c t ) to Form the signal x m ( t ). Compute the ±ourier TransForm oF x m ( t ) For ω c = 100 π rad/s. (c) Next, x m ( t ) is modulated with cos( ω c t + π/ 4). Determine what flter is needed (i.e., determine H ( ω )) to retrieve x ( t ) From this signal. 1...
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