Z – TRANSFORM PART – A 1. Define Z – transform of sequence Un. 2. Find Z [ an ] 3. Find Z [ n ] 4. Find Z [ c ], where c is any constant. 5. Find Z [ cos nθ ] 6. Find Z [ sin nθ ] 7. State Damping rule. 8. Define Z – transform of f(t) 9. Find Z [ eat ] 10. Find Z [ t ] 11. Find Z [ eat f(t) ] 12. State second shifting property of Z – transform. 13. State convolution theorem of Z – transform. 14. State final value theorem. 15. State initial value theorem. 16. Find Z [ 1 / n ] 17. Find Z [ 1 / n! ] 18. Find Z [ 1 / n ( n + 1) ] 19. Find Z [ 2 n2 + 3 n + 7 ] 20. Find Z [ np ] PART –B 21. Find Z [ an cos nθ ] and Z [an sin nθ ] 22. Find Z [an n2 ]. 23. Find Z [ cos nπ/2 ] and Z [ sin nπ/2 ] 24. Find the Z – transforms of the following (i) ean (ii) n ean 25. Find the Z – transform of (i) cosh nθ (ii) an cosh nθ 26. Find Z [ cos ( nπ/2 + π/4 ) ]
27. Find the Z – transform of (i) ncp
(ii)
n+p
cp
28. Find the Z – transform of unit impulse sequence and unit step sequence. 29. Find the Z – transform of (i) sinh nθ (ii) an sinh nθ 30. Find Z [ et sin2t ] and Z [ e-2t sin3t ]. 31. Find the inverse Z – transform of z / ( z + 1 )2 by division method. 32. Find the inverse Z – transform of { 2 z2 + 3z } / ( z + 2) ( z – 4 ) by partial fractions method. 33. Find the inverse Z – transform of ( z3 – 20 z ) / ( z – 2 ) 3 ( z – 4 ) by partial fraction method. 34. Find the inverse Z – transform of 10 z / ( z-1) ( z-2) by inversion integral method. 35. Find the inverse Z – transform of 2z / ( z -1 ) ( z - i ) ( z + I ) by inversion integral method. 36. Using convolution theorem , evaluate the inverse Z – transform of z2/ ( z -a ) ( z - b ) 37. Using convolution theorem , evaluate the inverse Z – transform of z2/ ( z –a) 2 38. Show that ( 1/ n! ) * (1/ n! ) = 2n / n! 39. Solve yn+2 + 6 y n+1 + 9yn = 2n with y0 = y1 = 0, using Z – transform. 40. Solve yn+2 - 2 y n+1 + yn = 3n + 5.