tutorial4 - π + + 6 2 10 4 t cos b) waveform in Q5 of...

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EE3118 Linear Systems and Signal Analysis KST SemA 2008/09 Tutorial 4 Q1. Determine the Fourier Transforms of the signals shown as below. You may use the Fourier Transform theorems and pairs in the notes. Q2. Determine the Fourier transform of the signum function sgn(x) as defined () < = 0 x if 1 0 x if 1 sgn x Q3. Assume that the Fourier Transform of the impulse response of a system is given as () < = rad/s 8 . 0 if 0 rad/s 8 . 0 0 if ) 8 . 0 ( π ω j e H a) Sketch the Bode diagram for the range of < 0 . b) Determine the steady-state output response of the system if x(t) in Q1 of Tutorial 3 is used as input. Q4. Consider the R-C network shown below, determine the steady state output () t v o if the input voltage () t v i is given by a)
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Unformatted text preview: π + + 6 2 10 4 t cos b) waveform in Q5 of Tutorial 3 Q4. Consider an LTI system with impulse response ( ) ( ) t u e t h t 4 − = Find the Fourier series representation of the steady state output y(t) for the following inputs a) ( ) ( ) t t x π = 2 cos b) ( ) ( ) ( ) ∑ ∞ −∞ = − δ − = n n n t t x 1 Q5. Consider a continuous-time LTI system with the following frequency response: ( ) ω + ω − = ω j a j a H where a&gt;0 . a) What are the values of magnitude ( ) ω H and phase ( ) ω ∠ H ? b) What is the impulse response of the system? c) What is the output if the input is ( ) ( ) t u e t x bt − = with &gt; b and a b ≠ ....
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