Name CM ECE 300 Signals and Systems Exam 3 May 2006 This exam is closed book in nature You are not to use a computer during the exam but you can use a calculator for simple calculations Problem 1 20 Problem 2 50 Problem 3 30 Exam 3 Total Score 100 1 Name CM 1 20 points Consider a causal linear time invariant system with impulse response given by h t e t 1 u t 1 The input to the system is given by x t u t u t 1 u t 3 Using graphical convolution determine the output y t for 2 t 5 Note the limited range of t we are interested in Specifically you must a Flip and slide h t b Show graphs displaying both h t l and x l for each region of interest c Determine the range of t for which each part of your solution is valid d Set up any necessary integrals to compute y t e Evaluate the integrals but do simplify your answers 2 Name CM 2 50 points Consider a linear time invariant system with transfer function given by 2e jw 2 w 4 H w else 0 3 3 t 1 cos 6 t 1 The output of the system is y t with input x t sinc p p a Determine X w b Sketch the spectrum of X w magnitude and phase accurately labeling the axes and important points c Determine the energy in x t d Sketch the spectrum of H w magnitude and phase accurately labeling the axes and important points e Determine y t the output of the system 3 Name CM 3 30 points Fill in the following table show all work x t a e t 2 5 2 b c X w cos w 2 jw 1 2 t 1 1 2 4 Name CM 5 Name CM 6 Name CM 7 Name CM 8 Name CM Some Potentially Useful Relationships T E lim x t T T 2 2 dt x t dt T 2 1 x t dt T 2T T P lim e jx cos x jsin x j 1 1 jx jx e e 2j 1 jx jx cos x e e 2 sin x 1 1 cos 2 x cos 2x 2 2 1 1 sin 2 x cos 2x 2 2 T T t t rect 0 u t t 0 u t t0 2 2 T 9
View Full Document
Unlocking...