Assign4_FourierTransform - signal: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛...

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EE3210 Assignment 4: Fourier Transform Due: (before lecture) Oct 28, 2009 (Marks will be deducted for late submission.) 1. Determine the Fourier transforms of the following continuous-time signals: a) ) 1 ( ) 1 ( 2 t u e t b) 1 2 t e Sketch and label the magnitude of each Fourier transform. 2. Prove the following time-shifting property of the continuous-time Fourier transform: ) ( ) ( 0 0 ω j X e t t x t j F ⎯→ . 3. Determine the Fourier transform of the following continuous-time periodic
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Unformatted text preview: signal: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + 4 2 sin π t . 4. Consider the Fourier transform pair 2 2 2 + ⎯→ ← − a a e F t a . Use appropriate Fourier transform properties to determine the Fourier transform of t j e t a a 2 2 2 2 − + . 5. Determine the Fourier transforms of the following discrete-time signals: a) ] 1 [ 2 1 1 − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − n u n b) ] 1 [ ] 1 [ + + − n n δ...
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