Unformatted text preview: j 2 πf ) of the signal x ( t ) = u ( t + 2)2 u ( t ) + u ( t1) Evaluate the magnitude  X ( jω )  and the phase arg( X ( jω )) at ω = π . Problem 4 (25 points) A periodic waveform x ( t ) has period 4. We know that the values taken by x ( t ) over the interval 100 ≤ t ≤ 104 are as follows: x ( t ) = ´ 1 100 ≤ t < 1031 103 ≤ t < 104 (a) 5 points Sketch x ( t ) over the interval4 ≤ t ≤ 4, labeling both axes carefully. (b) 10 points Find the complex exponential Fourier series { a k } for x ( t ) and specify the value of the fundamental frequency ω in radians/sec. Simplify your expression for the Fourier series coe±cients as much as possible. (c) 10 points Find the output y ( t ) when x ( t ) is passed through a ﬁlter with impulse response h ( t ) = sinc( t 6 )....
View
Full Document
 Fall '07
 MADHOW
 Fourier Series, Complex number, Midterm Examination Problems

Click to edit the document details