Tuto8_Filtering_Modulation - Find the Fourier series...

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EE3210 Tutorial 8: Filtering and Modulation 1. Consider a causal 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 = . a) Determine its frequency response. b) Use the result in part (a) to determine its magnitude response, | H ( e j ω )|. c) Is it a low-pass, band-pass or high-pass filter? Justify your answer. d) Consider the following signal: 4 3 sin n π . Find its fundamental period, its fundamental frequency and its Fourier series representation. e) Suppose that the signal in part (d) is the input to the system described above.
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Unformatted text preview: Find the Fourier series representation of the corresponding output. 2. An information signal x ( t ) is modulated by cos 120 t. We denote the modulated signal by r ( t ), where r ( t ) = x ( t ) cos 120 t. Now we know that t t t t r 130 cos 2 120 cos 8 110 cos 2 ) ( + + = . a) Determine the Fourier transform of r ( t ). Sketch it as a function of . b) Determine the Fourier transform of x ( t ). Sketch it as a function of . c) Hence, or otherwise, determine x ( t )....
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