EE422G Review 21. Given the initial condition problem (1) What is its solution? (2) Prove it. (Note: tattadttftfdtfdtd),(),(),()2. System’s initial condition, state equation, and output equation are given byFind the Laplace transform of the output.3. What is 11)( ASIL where A is a square matrix.4. Find te 5610using two different methods.5A. Obtain a state model for the network5B. Example 7-76. Obtain a state model for the system defined by (1) )3(1)()(ssssUsY(2) 3)3(1)()(sssUsY7. x(t) is a continuous time signal. Its Fourier transform is X(f). xs(t) is the sampled signal of x(t) by using the sampling function p(t) with sampling period T. Denote2/2/2)(1TTtfjnndtetpTCs where fs =1 / T. Prove nsnsnffXCfX )()(8. Give the mapping of the following regions / points in s-plane to z-plane:(1) left hand s-plane; (2) right hand s-plane; (3) jw axis; (4) s=09. Find the z-transform of otherwisenn0 01)(, 0001)(nnnu, and)0,0()()( neenTxnTnT00)( xtxBuAxx)()()(0)0(),()()(tDutCxtyxtButAxtx10. Memorize z-transform pairs No. 1 to No. 5 in Table 8-1.11. Given 111)(zeeZTnT. Prove 211)1()(zTznTZ and211)1()(zezTenTeZTTnT12. Determine the z-transform for the following sequences of samples (A) )(51)( nunTxn(B) )(1)( nusnTxn(C) )4(43)()( nununTxn(D) )8(2)(2)( nununTx(E) )4(32)( nunTxn(F) )4(32)(4nunTxn13. Find the inverse Z-transform for (a) )2.01)(1(2)(11 zzzX (b) )1)(1(2)(11 zzzX(c) )4.01)(2.01(3.01)(111zzzzX (d) )4.02)(2.01(3.01)(111zzzzX(e) 211)5.01)(1(1)(zzzX (f) 21)81.01(1)(zzX(g) 281.011)(ZZX (h) )25.0)(5.0()(2zzzzzX14. Find )(*)()( nThnTxnTy where )3(41)( nunTxnand )5(31)( nunThn15. Determine H(Z) and h(nT) for following systems(a) )()()( nTxTnTynTy (b) )3(3)()2()(2)( TnTxnTxTnTyTnTynTy 16. Determine the range of K which ensures the following systems stable:(a) )()2()()(2nTxTnTyKTnTKynTy (b) )()2()(2)(2nTxTnTyKTnTKynTy 17. Find the frequency response for the system: )2()()( TnTxnTxnTy
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