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Assign5_FrequencyDomain - y n 3 Consider a continuous-time...

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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 ] [ π π 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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