Tutoral1_ans - EE 3008 Fourier Transform Tutorial Solutions...

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EE 3008. Fourier Transform Tutorial Solutions Q1) 2 () ( ) 2s i n ( ) / 2 s i n c jf T T t ee G fg t e d t A Af Tf A T f T ππ π −+ −∞ == = = Q2) (a) The above question shows that if we compress the time domain function by 4, then the frequency domain spectrum is expanded by a factor of 4. This can be generalized to any other factor. (b) The magnitude of the Fourier transform is the same as that for (a). (What is the Fourier transform?). Q3) (1) { } 0 2 0 ( ) t xt t X f e −= F . Its magnitude is the same as | X ( f )|. Since x ( t ) is real (so is x ( t t 0 )), its magnitude spectrum is symmetric to the y -axis. (2) { } 0 2 0 ( ) t xte X f f =− F . The magnitude spectrum is plotted below, which is no longer symmetric (since x ( t ) e j 2 f 0 t is not real). 0 t T/2 A -T/2 g(t) f AT 1/T -1/T 2/T -2/T |G(f)| 0 t T/8 A -T/8 g(t) f AT/4 4/T -4/T 8/T -8/T |G(f)| f 0 2 f c A
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Q4) (a) 2 0.001 22 0.001 0.001 3 ( ) 3 0.006sin (0.002 ) 2 jf t t t e X fx t e d t e d t c f π ππ +∞ + −−
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Tutoral1_ans - EE 3008 Fourier Transform Tutorial Solutions...

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