midterm_fall05

# midterm_fall05 - j 2 πf of the signal x t = u t 2-2 u t u...

This preview shows page 1. Sign up to view the full content.

UCSB Fall 2005 ECE 130A: Midterm Examination Problems INSTRUCTIONS: Problems are weighted as shown. Show your work. No credit without proper justification, even if your answers are correct. The exam is closed book, closed notes, except for the sheet of formulas provided separately. Problem 1 (20 points) This question has four unrelated parts. 1(a) 4 points A system with input x ( t ) has output y ( t ) = sin( π t ) e j | x ( t ) | Is the system stable? Is it time-invariant? 1(b) 4 points Evaluate the integral 1 - 1 δ ( t + 2) e t + δ ( t - 1 2 ) sin( π t ) dt 1(c) 7 points Sketch the following three signals as a function of time, carefully labeling the important points. x ( t ) = (1 - t )( u ( t ) - u ( t - 1)) x 1 ( t ) = x ( t - 2) + x (2 - t ) x 2 ( t ) = x 1 (5 + 2 t ) 1(d) 5 points Evaluate the integral -∞ sin 2 5 t t 2 dt Problem 2 (10 points) Let x ( t ) = e - 2 t u ( t ). Find and sketch the output y ( t ) = ( x * h )( t ) when x ( t ) is passed through a filter with impulse response h ( t ) = x ( - t ). Problem 3 (10 points) Find the Fourier transform X ( j ω ) or X
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: j 2 πf ) of the signal x ( t ) = u ( t + 2)-2 u ( t ) + u ( t-1) 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 < 103-1 103 ≤ t < 104 (a) 5 points Sketch x ( t ) over the interval-4 ≤ 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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern