Assign5_FrequencyDomain - y [ n ]. 3. Consider a...

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EE3210 Assignment 5: Fourier Transform Due: (before lecture) Nov 18, 2009 (Marks will be deducted for late submission.) 1. The input and the output of a stable and causal LTI system are related by the differential equation ) ( 9 ) ( 3 ) ( 8 ) ( 6 ) ( 2 2 t x dt t dx t y dt t dy dt t y d + = + + . a) Find the frequency response of this system. b) Find the impulse response of this system. c) What is the response of this system if [ ] ) ( ) ( 3 t u e e t x t t + = . 2. Consider a discrete-time LTI system whose input x[n] and output y[n] are related by the following difference equation: ] [ ] 1 [ 4 1 ] [ n x n y n y = . Suppose that the input signal is given by: + = 6 5 cos 2 ] [ ππ n n x . a) Determine the frequency response of the system. b) What is the fundamental frequency of x [ n ]? Determine its Fourier series coefficients, { a k }. c) Find the Fourier series representation of the output
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Unformatted text preview: y [ n ]. 3. Consider a continuous-time LTI system S whose frequency response is ⎩ ⎨ ⎧ ≥ = otherwise , 250 , 1 ) ( ω j H . When the input to this system is a signal x ( t ) with fundamental period T = π /7 and Fourier series coefficients a k , it is found that the output y ( t ) is identical to x ( t ). For what values of k is it guaranteed that a k = 0? 4. Consider the following system, with t t c t c c ω cos ) ( ) ( 2 1 = = . The ideal low pass filter has cutoff frequency m , where c m << . Sketch | Y ( j )| and | Z ( j )|. Identify all amplitudes and frequencies of importance. 1 ) ( j M m 1 −ω m × × x ( t ) y ( t ) z ( t ) Ideal Low Pass Filter m t ( ) c 1 t c 2 t ( ) ( )...
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Assign5_FrequencyDomain - y [ n ]. 3. Consider a...

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