Q.1 Choose the correct answer 1. The following function represents a) Even function b) Odd function c) Neither odd nor even d) No one of the above 2. The
... [Show More] following function represents a) Even function b) Odd function c) Neither odd nor even d) No one of the above 3. The following figure can be represented by a) ๐(๐) = {โฆ . . , 0,2,0, โฆ .} b) ๐ฆ(๐) = { โฆ . . ,0, 2,4,0, โฆ . โ } c) ๐ฆ(๐) = {2,4, 0, โฆ .} d) ๐, ๐ Question Bank Ministry of Higher Level 300- signal Analysis โ ELE 271 Education The High Inst. Of Eng. & Tech. at Mansoura Contact: royfields212@gmail.com 4. The following figure can be represented by a) ๐ข(๐) b) ๐ข(๐ โ ๐) c) ๐ฟ(๐) d) ๐ฟ(๐ โ ๐) 5. ๐น(๐๐) = ๐๐น(๐) a) True b) false 6. ๐น(๐๐)= a) 1 |๐| ๐ฟ(๐ก) b) ๐ ๐ฟ(1/๐ก) c) โ๐ ๐ฟ(๐ก) d) 1 ๐ ๐ฟ(๐ก) 7. โซ ๐(๐) ๐ โ๐ ๐น(๐) ๐
๐= a) 0 b) Not defined c) ๐ฅ(0) d) ๐๐ ๐๐๐ ๐๐ ๐กโ๐ ๐๐๐๐ฃ๐ 8. โซ ๐(๐) ๐ ๐ ๐น(๐) ๐
๐= a) 0 b) Not defined c) ๐ฅ(0) 9. โซ ๐(๐) ๐ โ๐ ๐น(๐) ๐
๐= a) 0 b) Not defined c) ๐ฅ(0) 10. If ๐(๐) = ๐ โ๐๐ ๐(๐) then ๐(๐) ๐๐ a) Power signal b)Energy signal c) Neither power nor signal 11.If ๐[๐] = (โ๐. ๐) ๐ ๐[๐] then ๐(๐) ๐๐ a) Power signal b)Energy signal c) Neither power nor signal 12.If ๐[๐] = ๐ ๐(๐) then ๐(๐) ๐๐ a) Power signal b)Energy signal c) Neither power nor signal 13.If the signal, ๐[๐] = ๐๐จ๐ฌ ๐
๐ ๐ + ๐ฌ๐ข๐ง ๐
๐ ๐ then the fundamental period is a) ๐๐ = 6 b) ๐๐ = 48 c) ๐๐ = 24 d) ๐๐ = 8 14.Is the ๐[๐] = ๐๐จ๐ฌ ๐ ๐ ๐ is periodic a) True b) False 15.If the signal, ๐(๐) = ๐ ๐[( ๐
๐ )๐โ๐] then the fundamental period is e) ๐๐ = 4 f) ๐๐ = 5 g) ๐๐ = 24 h) ๐๐ = 8 16. For LTI system, ๐[๐] โ ๐น[๐] = a) ๐ฟ[๐] b) ๐ฅ[๐] c) ๐ฅ[๐ โ 1] d) ๐ฟ[๐ โ 1] 17. For LTI system, if ๐[๐] = ๐น[๐] + ๐น[๐ โ ๐] + ๐น[๐ โ ๐] + ๐น[๐ โ ๐], ๐[๐] = ๐น[๐] + ๐น[๐ โ ๐] + ๐น[๐ โ ๐] then ๐[๐] = a) ๐ฆ[๐] = { โฆ โฆ โฆ โฆ . . , ๐, ๐, ๐, ๐, ๐, ๐, ๐ โฆ . โ } b) ๐ฆ[๐] = {๐, ๐, ๐, ๐, ๐} c) ๐ฆ[๐] = {. . , ๐, ๐, ๐, ๐, ๐, ๐, ๐, โฆ }} d) ๐ฆ[๐] = { โฆ โฆ โฆ โฆ โฆ . , ๐, ๐, ๐, ๐, ๐, ๐, ๐, ๐ โฆ . โ } 18. For LTI system, if๐(๐) = โซ ๐ โ(๐โ๐) ๐(๐)๐
๐, ๐ โโ impulse response is a) โ(๐ก) = ๐ โ2๐ก b) โ(๐ก) = ๐ โ๐กu(t) c) โ(๐ก) = ๐ โ2๐ก๐ข(๐ก) d) โ(๐ก) = ๐ โ๐ก 19. For LTI system, if๐(๐) = โซ ๐ โ(๐โ๐) ๐(๐)๐
๐, ๐ โโ Eigen value is a) ๐ = 1 ๐ + 1 b) ๐ = 1 ๐ c) ๐ = 1 ๐ +1 d) ๐ = ๐ +1 ๐ 20.If ๐[๐] = ( ๐ ๐ ) ๐ ๐[๐ โ ๐] then a) System is causal not stable b) System is stable not causal c) System is causal and stable d) System is not causal and not stable 21. For LTI system, ๐[๐] = ๐[๐] โ ๐๐[๐ โ ๐] + ๐[๐ โ ๐] the system is a) Recursive and IIR system b) Recursive and FIR system c) Non-Recursive and FIR system d) Non-Recursive and IIR system 22. For LTI system, ๐[๐] + ๐๐[๐ โ ๐] = ๐[๐] + ๐[๐ โ ๐] the system is a) Recursive and IIR system b) Recursive and FIR system c) Non-Recursive and FIR system d) Non-Recursive and IIR system 23. Laplace transform for x(t) can be calculated from the relation a) ๐(๐ ) = โซ ๐ฅ(๐ก)๐ โ ๐ ๐ก โโ ๐๐ก b) ๐(๐ ) = โซ ๐ฅ(๐ก)๐ โ โ๐ ๐ก 0 ๐๐ก c) ๐(๐ ) = โซ ๐ฅ(๐ก)๐ โ ๐ ๐ก 0 ๐๐ก d) ๐(๐ ) = โซ ๐ฅ(๐ก)๐ โ โ๐ ๐ก โโ ๐๐ก 24. Laplace inverse of ๐ฟ(๐) = ๐๐+๐ ๐+๐ ,๐น๐(๐) > โ๐ a) ๐ฅ(๐ก) = 2๐ฟ(๐ก) โ 3๐ โ๐ก๐ข(๐ก) b) ๐ฅ(๐ก) = 2๐ฟ(๐ก) + 3๐ โ2๐ก๐ข(๐ก) c) ๐ฅ(๐ก) = 2๐ฟ(๐ก) โ 3๐ โ2๐ก๐ข(๐ก) d) ๐ฅ(๐ก) = โ2๐ฟ(๐ก) โ 3๐ โ๐ก๐ข(๐ก) 25. Laplace inverse of ๐ฟ(๐) = ๐ ๐+๐๐+๐ ๐ ๐+๐๐+๐ ,๐น๐(๐) > โ๐ a) ๐ฅ(๐ก) = ๐ฟ(๐ก) + (2๐ โ๐ก + ๐ โ2๐ก )๐ข(๐ก) b) ๐ฅ(๐ก) = 2๐ฟ(๐ก) + 3๐ โ2๐ก๐ข(๐ก) c) ๐ฅ(๐ก) = (2๐ โ๐ก + ๐ โ2๐ก )๐ข(๐ก) d) ๐ฟ(๐ก) + (2๐ โ๐ก + ๐ โ2๐ก ) 26. LTI system is causal if a) ๐
๐๐ถ: ๐
๐(๐ ) > ๐๐๐๐ฅ b) ๐
๐๐ถ: ๐
๐(๐ ) < ๐๐๐๐ฅ c) โ(๐ก) = 0 ๐๐๐ ๐ก < 0 d) a, c 27. LTI system is stable if a) ๐
๐๐ถ ๐๐ ๐ป(๐ )๐๐๐๐ก๐๐๐ ๐๐ค โ ๐๐ฅ๐๐ b) ๐
๐๐ถ: ๐
๐(๐ ) > ๐๐๐๐ฅ c) ๐
๐๐ถ: ๐
๐(๐ ) < ๐๐๐๐ฅ d) โ(๐ก) = 0 ๐๐๐ ๐ก < 0 28. Laplace Transform for ๐(๐) = ๐(๐) a) X(s)=1 ๐ , ๐
๐๐ถ: ๐
๐(๐ ) > 0 b) X(s)=1 ๐ , ๐
๐๐ถ: ๐
๐(๐ ) < 0 c) X(s)=๐ , ๐
๐๐ถ: ๐
๐(๐ ) > 0 d) X(s)=๐ , ๐
๐๐ถ: ๐
๐(๐ ) > 0 29. Laplace Transform for ๐(๐) = ๐ โ๐๐๐(๐) a) X(s)= 1 ๐ โ2 , ๐
๐๐ถ: ๐
๐(๐ ) > โ2 b) X(s)=1 ๐ , ๐
๐๐ถ: ๐
๐(๐ ) < โ2 c) X(s)= 1 ๐ +2 , ๐
๐๐ถ: ๐
๐(๐ ) > โ2 d) X(s)= 1 ๐ +2 , ๐
๐๐ถ: ๐
๐(๐ ) < โ2 30. Laplace Transform for ๐(๐) = ๐(๐ โ ๐) a) X(s)=๐ โ3๐ ๐ , ๐
๐๐ถ: ๐
๐(๐ ) > 0 b) X(s)=๐ 3๐ ๐ , ๐
๐๐ถ: ๐
๐(๐ ) < 0 c) X(s)=๐ 3๐ ๐ ,๐
๐๐ถ: ๐
๐(๐ ) > 0 d) X(s)=๐ , ๐
๐๐ถ: ๐
๐(๐ ) > 0 31. Laplace Transform for ๐(๐) = ๐ ๐๐๐(โ๐) a) X(s)= โ1 ๐ +3 , ๐
๐๐ถ: ๐
๐(๐ ) > โ3 b) X(s)= โ1 ๐ โ3 , ๐
๐๐ถ: ๐
๐(๐ ) < 3 c) X(s)= 1 ๐ โ3 , ๐
๐๐ถ: ๐
๐(๐ ) > โ3 d) X(s)= 1 ๐ โ3 , ๐
๐๐ถ: ๐
๐(๐ ) < 3 32. If systems do not have a bounded output for bounded input, then the system is said to be a) Causal b) Non-causal c) Stable d) Non-stable 33. The system described by the input-output equations y(n)=x(-n) is a causal system. a) True b) False Explanation: For n=-1, y(-1)=x(1) That is, the output of the system at n=-1 is depending on the future value of the input at n=1. So the system is a non-causal system. 34. If the output of the system of the system at any โnโ depends only the present or the past values of the inputs, then the system is said to be a) Linear b) Non-Linear c) Causal d) Non-causal 35. The system described by the input-output equations y(n)=x2 (n) is a Non-linear system. a) True b) False Explanation: Given equation is y(n)=x2 (n) Let y1(n)=x1 2 (n) and y2(n)=x2 2 (n) Y3(n)=y1(n)+y2(n)= x1 2 (n)+ x2 2 (n)โ (x1(n)+x2(n))2 So the system is non-linear 36. Whether the system described by the input-output equations y(n)=x(n)-x(n-1) a Time-variant system. a) True b) False Explanation: If the input is delayed by k units then the output will be y1(n)=x(n-k)-x(n-k-1) If the output is delayed by k units then y(n-k) = x(n-k)-x((n-k)-1) => y1(n)=y(n-k). Hence the system is time-invariant. 37. The system described by the input-output equation y(n)=nx(n)+bx3 (n) is a __________ a) Memory-less system b) Linear system c) Identical system d) None of the mentioned 38. The block denoted as follows is known as __________ a) Delay block b) Advance block c) Multiplier block d) Adder block 39. The discrete time function defined as u(n)=n for nโฅ0; u(n)=0 for n<0 is an _____________ a) Unit sample signal b) Unit step signal c) Unit ramp signal d) None of the mentioned 40. The function given by the equation x(n)=1, for n=0; x(n)=0, for nโ 0 is a _____________ a) Step function b) Ramp function c) Triangular function d) Impulse function 41. Resolve the sequence into a sum of weighted impulse sequences. a) 2ฮด(n)+4ฮด(n-1)+3ฮด(n-3) b) 2ฮด(n+1)+4ฮด(n)+3ฮด(n-2) c) 2ฮด(n)+4ฮด(n-1)+3ฮด(n-2) d) None of the mentioned 42. The formula y(n)=โ ๐ฑ(๐ค)๐ก(๐ง โ ๐ค) โ ๐=โโ That gives the response y(n) of the LTI system as the function of the input signal x(n) and the unit sample response h(n) is known as ______________ a) Convolution sum b) Convolution product c) Convolution Difference d) None of the mentioned 43. Determine the output y(n) of a LTI system with impulse response h(n)=an u(n), |a|<1with the input sequence x(n)=u(n). a) 1โ๐ ๐+1 1โ๐ b) 1โ๐ ๐โ1 1โ๐ c) 1โ๐ ๐+1 1+๐ d) None of the mentioned 44. An LTI system is said to be causal if and only if? a) Impulse response is non-zero for positive values of n b) Impulse response is zero for positive values of n c) Impulse response is non-zero for negative values of n d) Impulse response is zero for negative values of n 45. x(n)*ฮด(n-no)=? a) x(n+no) b) x(n-no) c) x(-n-no) d) x(-n+no) 46. Is the system with impulse response h(n)=2nu(n-1) stable. a) True b) False 47. The system described by the equation y(n)=ay(n+1)+b x(n) is a recursive system. a) True b) False Explanation: Since the present output depends on the value of the future output, the system is not called a Recursive system. 48. The system described by the equation y(n)=ay(n-1)+b x(n) is a recursive system. a) True b) False Explanation: Since the present output depends on the value of the previous output, the system is called a Recursive system. 49. The Z-Transform X(z) of a discrete time signal x(n) is defined as a) โ ๐ฅ(๐) โ ๐=โโ ๐ง ๐ b) โ ๐ฅ(๐) โ ๐=โโ ๐ง โ๐ c) โ ๐ฅ(๐) โ ๐=0 ๐ง ๐ d) None of the mentioned 50. What is the z-transform of the following finite duration signal? a) 2 + 4z + 5z2 + 7z3 + z4 b) 2 + 4z + 5z2 + 7z3 + z5 c) 2 + 4z-1 + 5z-2 + 7z-3 + z-5 d) 2z2 + 4z + 5 +7z-1 + z-3 51. What is the ROC of the signal x(n)=ฮด(n-k), k>0? a) z=0 b) z=โ c) Entire z-plane, except at z=0 d) Entire z-plane, except at z=โ 52. What is the z-transform of the signal x(n)=(0.5)nu(n)? a) 1/(1โ0.5๐งโ1) ,๐
๐๐ถ: |๐ง|>0.5 b) 1/(1โ0.5๐งโ1) ,๐
๐๐ถ: |๐ง|<0.5 c) 1/(1+0.5๐งโ1) ,๐
๐๐ถ: |๐ง|>0.5 d) 1/(1+0.5๐งโ1) ,๐
๐๐ถ: |๐ง|<0.5 53. Which of the following series has an ROC as mentioned below? a) a-n u(n) b) a-n u(-n) c) an u(n) 54. What is the z-transform of the signal x(n) = -a n u(-n-1)? a) 1/(1โa๐ง โ1 ) ROC |z|<|a| b) โ1/(1+a๐ง โ1 ) ROC |z|<|a| c) โ1/(1โa๐ง โ1 ) ROC |z|>|a| d) โ1/(1โa๐ง โ1 ) ROC |z|<|a| 55. What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)? a) |a|<|z|<|b| b) |a|>|z|>|b| c) |a|>|z|<|b| d) |a|<|z|>|b| 56. What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable? a) Entire z-plane, except at z=0 b) Entire z-plane, except at z=โ c) Contain unit circle d) None of the mentioned Explanation: if the system is stable, then H(z) converges for z=ejฯ. That is, for a stable discrete time LTI system, ROC of H(z) must contain the unit circle |z|=1. 57. Is the discrete time LTI system with impulse response h(n)=an u(n) (|a| < 1) BIBO stable? a) True b) False Explanation: The z-transform of h(n) is H(z)=๐ง/(๐งโ๐), ROC is |z|>|a| If |a|<1, then the ROC contains the unit circle. So, the system is BIBO stable. 58. Which of the following justifies the linearity property of z-transform? [x(n)โX(z)]. a) x(n)+y(n) โ X(z)Y(z) b) x(n)+y(n) โ X(z)+Y(z) c) x(n)y(n) โ X(z)+Y(z) d) x(n)y(n) โ X(z)Y(z) Explanation: According to the linearity property of z-transform, if X(z) and Y(z) are the z-transforms of x(n) and y(n) respectively then, the z-transform of x(n)+y(n) is X(z)+Y(z). 59. What is the z-transform of the signal x(n)=[3(2n )-4(3n )]u(n)? a) 3 1โ2๐งโ1 - 4 1โ3๐งโ1 b) 3 1โ2๐งโ1 - 4 1โ3๐ง+1 c) 3 1โ2๐ง - 4 1โ3๐ง d) None of the mentioned 60. What is the z-transform of the signal x(n)=sin(ฯn) u(n)? a) ๐ โ๐ ๐๐๐(๐) ๐+๐โ๐ ๐๐๐(๐)+๐โ๐ b) ๐ โ๐ ๐๐๐(๐) ๐โ๐โ๐ ๐๐๐(๐)โ๐โ๐ c) ๐ โ๐ ๐๐๐(๐) ๐+๐โ๐ ๐๐๐(๐)+๐โ๐ d) ๐ โ๐ ๐๐๐(๐) ๐โ๐โ๐ ๐๐๐(๐)+๐โ๐ 61. According to Time shifting property of z-transform, if X(z) is the ztransform of x(n) then what is the z-transform of x(n-k)? a) zk X(z) b) z - k X(z) c) X(z-k) d) X(z+k) 62. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)? a) 1+z N 1+zโ1 b) 1โz N 1+zโ1 c) 1+z โN 1+zโ1 d) 1โz โN 1โzโ1 63. What is the z-transform of the signal x(n)=na n u(n) ? a) (๐๐) โ๐ (๐โ(๐๐)โ๐) ๐ b) ๐๐โ๐ (๐โ(๐๐)โ๐) ๐ c) ๐๐โ๐ (๐โ๐๐โ๐) ๐ d) ๐๐โ๐ (๐+๐๐โ๐) ๐ 64. X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal n x(n)? a) -z ๐
๐(๐) ๐
๐ b) z๐
๐(๐) ๐
๐ c) -z -1๐
๐(๐) ๐
๐ d) z-1๐
๐(๐) ๐
๐ 65. If X(z) is the z-transform of the signal x(n), then what is the ztransform of the signal x(-n)? a) X(-z) b) X(z-1 ) c) X-1 (z) d) None of the mentioned 66. If Z{x1(n)}โX1(z) and Z{x2(n)} โX2(z) then Z{x1(n)*x2(n)}=? a) X1(z).X2(z) b) X1(z)+X2(z) c) X1(z)*X2(z) d) None of the mentioned 67. What is the z-transform of the signal x(n)=ฮด(n-n0)? a) ๐ง ๐๐ b) ๐ง โ๐๐ c) ๐ง (๐โ๐๐) d) ๐ง (๐+๐๐) 68. What is the z-transform of the signal x(n)=[5(3n )-9(7n )]u(n)? a) 5 1โ3๐โ1 - 9 1โ7๐โ1 b) 5 1+3๐โ1 - 9 1+7๐โ1 c) 5 1โ3๐ - 9 1โ7๐ d) None of the mentioned 69. Which of the following method is used to find the inverse z-transform of a signal? a) Direct from table b) Expansion into a series of terms c) Partial fraction expansion d) All of the mentioned 70. What is the partial fraction expansion of X(z) = ๐ (๐+๐โ๐)(๐โ๐โ๐) ๐ ? a) ๐ 4(๐+1) + 3๐ 4(๐โ1) + ๐ 2(๐+1) 2 b) ๐ 4(๐+1) + 3๐ 4(๐โ1) - ๐ 2(๐+1) 2 c) ๐ 4(๐+1) + 3๐ 4(๐โ1) + ๐ 2(๐โ1) 2 d) ๐ 4(๐+1) + ๐ 4(๐โ1) + ๐ 2(๐+1) 2 71. What is the causal signal x(n) having the z-transform X(Z)= ๐ (๐+๐โ๐)(๐โ๐โ๐) ๐ ? a) [ 1 4 (-1)n + 3 4 - ๐ 2 ] u(n) b) [ 1 4 (-1)n + 3 4 - ๐ 2 ] u(-n-1) c) [ 1 4 + 3 4 (-1)n - ๐ 2 ] u(n) d) [ 1 4 (-1)n + 3 4 + ๐ 2 ] u(n) 72. What is the partial fraction expansion of X(z) = ๐ ๐โ๐.๐๐โ๐+๐.๐๐โ๐ ? a) 2๐ ๐โ1 - ๐ ๐+0.5 b) 2๐ ๐โ1 + ๐ ๐โ0.5 c) 2๐ ๐โ1 + ๐ ๐+0.5 d) 2๐ ๐โ1 - ๐ ๐โ0.5 73. What is the inverse z-transform of X(z)= ๐ ๐โ๐.๐๐โ๐+๐.๐๐โ๐ if ROC is 0.5<|z|<1? a) -2u(-n-1)+(0.5)nu(n) b) -2u(-n-1)-(0.5)nu(n) c) -2u(-n-1)+(0.5)nu(-n-1) d) 2u(n)+(0.5)nu(-n-1) 74. What is the inverse z-transform of X(z)= ๐ ๐โ๐.๐๐โ๐+๐.๐๐โ๐ if ROC is |z|<0.5? a) [-2-0.5n ]u(n) b) [-2+0.5n ]u(n) c) [-2+0.5n ]u(-n-1) d) [-2-0.5n ]u(-n-1) 75. What is the inverse z-transform of X(z)= ๐ ๐โ๐.๐๐โ๐+๐.๐๐โ๐ if ROC is |z|>1? a) (2-0.5n )u(n) b) (2+0.5n )u(n) c) (2n-0.5n )u(n) d) None of the mentioned 76. What is the proper fraction and polynomial form of the improper rational transform? X(Z) = ๐+๐๐ โ๐+ ๐๐ ๐ ๐ โ๐+ ๐ ๐ ๐ โ๐ ๐+ ๐ ๐ ๐โ๐+ ๐ ๐ ๐โ๐ a) = 1 + 2๐ โ1 + 1 6 ๐ โ1 1+ 5 6 ๐โ1+ 1 6 ๐โ2 b) = 1 โ 2๐ โ1 + 1 6 ๐ โ1 1+ 5 6 ๐โ1+ 1 6 ๐โ2 c) = 1 + 2๐ โ1 + 1 3 ๐ โ1 1+ 5 6 ๐โ1+ 1 6 ๐โ2 d) = 1 + 2๐ โ1 โ 1 6 ๐ โ1 1+ 5 6 ๐โ1+ 1 6 ๐โ2 [Show Less]