143ahwk8

143ahwk8 - -t ) (b) x ( t ) = R t- sin(2 ) d . Hint: Recall...

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MAE 143 A: Signals and Systems. Homework #8 Assigned May 26. Due Jun 2 1. Look at the graphs of the signals in Figure 1. Can you say whether or not they are low-pass, high-pass or band-pass signals? Reason your answer. Figure 1: Signals corresponding to Problem 1 2. Find the Fourier transform of the following signals, using the tables and FT properties: (a) For x ( t ) = ± 2e ( - 1+ j 2 π ) t + 2e ( - 1 - j 2 π ) t ² u ( t ), find X ( ω ). (b) For x ( t ) = 1 . 6sinc 2 ( - t ) sin(4 πt ), find X ( f ) (c) For x ( t ) = e - t/ 4 u ( t ) * sin(2 πt ), find X ( f ) (d) For x ( t ) = d dt (sinc( t )), find X ( ω ) (e) For x ( t ) = R t -∞ rect( λ ) , find X ( ω ). 3. Plot the magnitude and phase spectrum of the following signals (you have to use FT tables and the FT properties in order to compute X ( ω )): (a) x ( t ) = sgn( t ) - sgn(
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Unformatted text preview: -t ) (b) x ( t ) = R t- sin(2 ) d . Hint: Recall that ( s ) is a real signal that is zero for s 6 = 0. 4. Compute the Impulse Response of each of the systems with the Frequency Response given next. Classify each Impulse Response as a low-pass, high-pass or band-pass signal. (a) H ( ) = 10 ( -1 2 ) + ( -1 2 (b) H ( ) =-2 ( ) * j ( ( -300)- ( + 300)) (c) H ( ) = 3sinc( f )e-j 2 f 5. Suppose a system Impulse Response is given by h ( t ) = 7( u ( t )-u ( t-20)). What is the FT of the system response to the signal x ( t ) = e-20 t u ( t )? 1...
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