32 p 301 so what this condition tests is whether the

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Unformatted text preview: he same answer. 1 + (2 − � )2 1 + (2 + � )2 t −j� (b) The signal x(t) depicted b elow: x(t) 1 ··· −1 −4 −5 −3 0 −2 5 2 3 1 4 ··· t −1 Note that the signal x(t) is composed of two time-shifted impulse trains, so we will use the following Fourier transform property and basic Fourier transform pair to find X (j� ) (see Tables 4.1 and 4.2, O&W, p.328-29): F x(t − to ) �� e −j�to X (j� ) , � � � � � 2ω � 2ωk α (t − nT ) �� α �− T k=−� T n=−� F 14 x(t) = x1 (t) + x2 (t) = � X (j� ) = � e −j� ⎩ 2ω −e 3 j� � � n=−� � � α (t − nT − 1) − � � n=−� � 2ωk α �− 3 k =−� 15 � α (t − nT + 1) , where T=3 � � �� 4ω 2ωk sin � = α �− . 3j 3 k =−� Problem 6 Determine the continuous-time signal corresponding to each of the following transforms: (a) X (j� ) = j [α (� + 1) − α (� − 1)] − 3 [α (� − ω ) + α (� + ω )] From the Fourier Transform of sinusoids in table 4.2 (O & W, p.3.29) F cos �0 t �� ω [α (� − �0 ) + α (� + �0 )] , F sin �0 t �� ω [α...
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This document was uploaded on 02/09/2014.

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