tutorial6 - = and ( ) = n y , n<0. Q6. Given the...

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EE3118 Linear Systems and Signal Analysis KST SemA 2008/09 Tutorial 6 Q1. Obtain the complete solution of each of the difference equations (i) () ( ) ( ) 8 2 8 1 6 = + n y n y n y , ( ) 2 0 = y , ( ) 5 1 = y (ii) () ( ) ( ) ( ) n n y n y n y 2 3 2 9 1 6 = + + , ( ) 0 0 = y , ( ) 4 1 = y Q2. Determine the output () nT y by solving the difference equation directly () () () () T nT y T nT y nT x nT y 2 16 9 2 3 + = when () 2 = nT x for n 0, () 0 0 = y and ( ) 5 . 0 = T y . Q3. Determine the output () n y by solving the following difference equation directly: () ( )( ) ( ) ( ) 1 3 2 80 1 8 + = + + n x n x n y n y n y , where () 1 0 = y , ( ) 2 1 = y for the input sequence ( ) ( ) n n x 3 . 0 4 = . Q4. Obtain the output () n y for the below difference equation () ( ) ( ) = + + 3 cos 4 2 09 . 0 1 6 . 0 n n y n y n y , where () 2 0 = y , () 5 1 = y . [Hints: ( ) () 2 3 cos 3 3 n j n j e e n K + = ] Q5. Consider the following linear difference equation: () () ()( ) 1 2 2 8 1 1 4 3 = + n x n y n y n y Determine the output () n y when ( ) ( ) n n x δ
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Unformatted text preview: = and ( ) = n y , n<0. Q6. Given the impulse response h(nT) and input sequence x(nT) as below, determine the output sequence by convolution sum. Q7. Assuming that the sampling time T=1 , the impulse response h(n) and the input x(n) are given as follows: ( ) ( ) ( ) ( ) ( ) 4 2 3 3 2 2 − − − + − − = n n n n n h ( ) ( ) ( ) n u n r n x − = 3 where u(n) is the discrete unit function, δ (n) is the discrete impulse function and ( ) < ≥ = n if n if n n r (a) Sketch h(n) and x(n) . (b) Determine the output sequence by calculating the convolution sum of h(n) and x(n) . n 1 2 h(nT 3 4 n -1 1 2 0 1 2 x(nT 3 4 -1 1 2 0...
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