Homework3 - EE 200 Fall 2009(Weber Homework 3 At the upper...

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EE 200 – Fall 2009 (Weber) Homework 3 At the upper right corner on page 1 of all homeworks, show: Last name, First name Date EE 200, Homework # Show intermediate steps whenever possible. 1. For each of the following systems defined below, indicate whether the sytem is linear, time invariant, both, or neither. You don’t have to show any proof of your answer, just indicate what type of system it is. a. y [ n ] = cos (2 πn ) x [ n ] e. y [ n ] = x [ n ] + 0 . 7 y [ n - 1] b. y [ n ] = cos (2 πn/ 7) x [ n ] f. y [ n ] = x [ n ] + 0 . 3( x [ n - 1]) 2 c. y [ n ] = cos (2 πn/ 7)( x [ n ] + x [ n - 1]) g. y [ n ] = 5 x [ n ] + 2 d. y [ n ] = x [ n ] + 0 . 7 x [ n - 1] h. y [ n ] = | x [ n ] | 2. A sampled signal is given by x [ n ] = 4 cos(0 . 3 πn - π/ 4) Find three continuous-time signals, x 1 ( t ), x 2 ( t ) and x 3 ( t ) of the form x ( t ) = A cos(2 πft + φ ) that when sampled at a sampling rate of f s = 1000 samples/sec. would each give this result. The frequencies of x 1 ( t ), x 2 ( t ) and x 3 ( t ) should all be below 1500Hz. 3. An AM modulated signal is given by the continuous time function x ( t ) = [5 + 3 cos(2 π 3000 t )] cos(2 π 10000 t ) a. Draw the spectrum of the signal labeling the frequencies. b. If we want to sample x ( t ) and avoid aliasing, what are the conditions on f s , the sampling frequency? 4. The impulse response of an LTI system is given by
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