hwk3 - 3 A system has a response that is the cube o± its...

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MAE 143 A: Signals and Systems. Homework #3. Assigned Jan 20. Due Jan 27. 1. For diferent systems, we observe the ±ollowing input-output experiments: (a) System 1: x ( t ) cos 2 (2 πf 0 t ) and 2 x ( t ) 1 + cos(4 πf 0 t ), ±or some constant f 0 . Is the system homogeneous? Why or why not? ( Hint: Use trigonometric ±ormulas to relate cos(4 πf 0 t ) and cos 2 (2 πf 0 t )) (b) System 2: x ( t ) cos(2 πt ) and x ( t - π 2 ) sin(2 πt ). Is the system time-invariant? Why or why not? ( Hint: Use trigonometric ±ormulas) (c) System 3: x ( t ) δ (2 t ) and 2 x ( t ) δ ( t ). Is the system homogeneous? Why or why not? 2. An amplitude-modulator system takes in an audio signal x ( t ) and returns the output signal: y ( t ) = cos(2 πω c t ) x ( t ) . Classi±y the sytem as to homogeneity, time-invariance, additivity, LTI, and memory.
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Unformatted text preview: 3. A system has a response that is the cube o± its excitation. That is, to a signal x ( t ), the system responds with the output y ( t ) = x ( t ) 3 . Classi±y the system as to homogeneity, time-invariance, invertibility, and memory. 4. An LTI system is excited by an input x ( t ) = 3ramp( t ) and produces the response y ( t ) = u ( t ), the unit-step ±unction. What will be the system response to g ( t ) = 2( t-1) u ( t-1)? Observe that we can compute this output because we can make use o± the LTI properties o± the system. 1...
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