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A#08-1 - waveform for which we have the Fourier transform...

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Assignment #8 ECSE-2410 Signals & Systems - Spring 2006 Due Tue 10/03/06 Using the properties and transform Tables (no integrations of the definition) find the Fourier transform, ) ( ϖ X , for the following signals: (a) ) ( t x = u ( t ) - u ( t - 2) (Express answer as a sinc function.) (b) ) ( t x = ) 1 ( - - t e u ( t -2) (c) ) ( t x = ( 29 ( 29 1 1 - - + t t δ δ (Write as a trig function.) (d) ( 29 4 cos ) ( π π + = t t x (e) ) ( t x = t e - [ u ( t ) - u ( t - 1)] (Express under a common denominator.) (f) ) ( t x = 1 - - t e (g) ( 29 - = t d t x τ πτ sinc ) ( (simplify answer) (h) (i) (j) One technique for finding Fourier transforms is to differentiate the signal until it reduces to a
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Unformatted text preview: waveform for which we have the Fourier transform in one of our Tables. Then the time differentiation property (or the integration property) can be used to find the transform of the original signal. Use this technique to find the Fourier transform of x ( t ) plotted below. 1-1 1 2 3-2-1 t x ( t ) x ( t ) 1 2 3-2-1 t 1 2-2 x ( t ) 1 1 3-2-1 t 1 2...
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