Tutorial1 - (See T2.23 and T2.25.) Q5) Suppose the two...

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EE 3008. Fourier Transform Tutorial Questions Q1) The Fourier transform of x ( t ) is defined as = dt e t x f X ft j π 2 ) ( ) ( X ( f ) is also called the spectrum of x ( t ). Find the Fourier transform of the following function. Draw its magnitude. Q2) Draw the magnitude of the Fourier transform of the following two functions. Q3) Suppose that x ( t ) is real and its magnitude spectrum is given below. (1) Determine the magnitude spectrum of x ( t t 0 ). Is it symmetric to the y -axis? Why? (2) Determine the magnitude spectrum of x ( t ) e j 2 f c t . Is it symmetric to the y -axis? Why? f A - f c 0 f c 0 t T/2 A -T/2 g(t) T 0 t A f(t) T/4 0 t A h(t) T/4 b (b) (a) | X ( f )|

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Q4) Determine the frequency domain expression for each of the two waveforms below and draw their magnitude and energy spectra.
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Unformatted text preview: (See T2.23 and T2.25.) Q5) Suppose the two waveforms in Q4 are passed through a filter with transfer function shown below. For each of the two waveforms, draw the magnitude spectrum and energy spectra at the filter’s output. (See T2.26.) Q6) (1) Derive the Fourier transform of 1; (2) Derive the Fourier transforms of sin(2 π f t ) and cos(2 π f t ); (3) Let X ( f ) be the Fourier transform of x ( t ). Determine the Fourier transforms of x ( t )sin(2 π f t ) and x ( t )cos(2 π f t ). -500 0 500 Hz H ( f ) 1 0 1 2 msec msec (b) 1 volts 2 volts 3 volts -1 0 1 msec msec (a)...
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This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.

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Tutorial1 - (See T2.23 and T2.25.) Q5) Suppose the two...

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