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hwk1 - (b the signal in ±igure E43 as a sum of shifted...

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MAE 143 A: Signals and Systems. Homework #1. Assigned Jan 6. Due Jan 13 1. Sketch the following continuous-time signals. You should draw by hand (do not use MATLAB or a calculator) after reasoning how the signals look like. (a) g ( t ) = u ( t + 1) - 2 u ( t - 1) + u ( t - 3), where u ( t ) is the unit step function. (b) g ( t ) = ( t + 1) u ( t - 1) - tu ( t ) - u ( t - 2), where u ( t ) is the unit step function. (c) g ( t ) = 3 δ (3 t ) + 6 δ (4( t - 2)) 2. Given the graphical definition of a function in figure E.45 (a) (see the book, Chapter 2), graph the transformations: (a) g (2 t + 1) (b) - 3 g ( - t ) 3. Describe the following signals in the Book, Chapter 2 (section on exercises): (a) the signal in Figure E42 as a ramp function minus a summation of step functions
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Unformatted text preview: (b) the signal in ±igure E43 as a sum of shifted semicircles. 4. ±or each of the following functions, decide whether it is periodic and, if it is, Fnd the fundamental period. (a) g ( t ) = 14 + 40 cos(60 πt ) (b) g ( t ) = 28 sin(400 πt ) + 12 cos(500 t ) (c) g ( t ) = sin(3 πt ) + cos(5 πt-3 π 4 ) 5. Compute: (a) the energy of the signal x ( t ) = 2rect( t ) + 1 2 rect( t-1 2 ) (b) the average signal power of the signal x ( t ) = 3 cos(2 πt + 30) (c) the energy of the signal x ( t ) = e (-1-j 8 π ) t u ( t ), where u ( t ) is the unit step function. 1...
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  • Summer '08
  • MIROSLAVKRSTIC
  • Summation, Heaviside step function, Elementary special functions, Rectangular function, Ramp function

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