Quiz1_sol - [ ] ) ( ) ( ) ( ) ( ) ( 2 1 2 1 t by t ay t bx...

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EE3210 Signal and Systems Quiz 1 (Solution) Semester A, 2009/10 1. (a) Not periodic. (b) Periodic, fundamental period = 14. 2. {} [] 2 / ) ( ) sin( ) ( ) sin( ) ( t u t t u t t x Ev = . -10 -8 -6 -4 -2 0 2 4 6 8 10 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 3. (a) Invertible. Inverse system: y [ n ] = x [2– n ] (b) Not invertible. Example: both ] 1 [ ] [ + n n δ and ] [ n give the same output ] [ n . 4. The energy of the signal is given by [] 25 ] 4 [ 16 ] [ 9 ] 4 [ 4 ] [ 3 2 2 2 = + = + = −∞ = −∞ = n n n n n n E δδ
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5. The system is: i. Causal . Because the output at time t does not depend on input at time greater than t . ii. Linear . Let the input be ) ( ) ( ) ( 2 1 t bx t ax t x + = . The corresponding output is
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Unformatted text preview: [ ] ) ( ) ( ) ( ) ( ) ( 2 1 2 1 t by t ay t bx t ax t t y + = + = where y 1 ( t ) and y 2 ( t ) are the outputs corresponding to inputs x 1 ( t ) and x 2 ( t ), respectively. Hence, the system is linear. iii. Not Time Invariant . Let y ( t ) be the output corresponding to x ( t ). Suppose the input is shifted by t , i.e., x ( t-t ). The corresponding output is t x ( t-t ) ≠ y ( t-t ) . 6. y 2 ( t ) is sketched below: 3 2 1 1 t y 2 ( t ) 2...
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This note was uploaded on 11/22/2009 for the course ELECTRONIC EE3210 taught by Professor Sungchiwan during the Spring '09 term at École Normale Supérieure.

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Quiz1_sol - [ ] ) ( ) ( ) ( ) ( ) ( 2 1 2 1 t by t ay t bx...

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