Multiple Choice Questions and Answers on Inverse Systems and Deconvolution

1. If the frequency response of an FIR system is given as H(z)=1-z-1-6z-2, then the system is ___________
a) Minimum phase
b) Maximum phase
c) Mixed phase
d) None of the mentioned
Answer: Maximum phase

2. An IIR system with system function H(z)=B(z)A(z) is called a minimum phase if ___________
a) All poles and zeros are inside the unit circle
b) All zeros are outside the unit circle
c) All poles are outside the unit circle
d) All poles and zeros are outside the unit circle
Answer: All poles and zeros are inside the unit circle

3. If the frequency response of an FIR system is given as H(z)=6+z-1-z-2, then the system is ___________
a) Minimum phase
b) Maximum phase
c) Mixed phase
d) None of the mentioned
Answer: Minimum phase

4. If the frequency response of an FIR system is given as H(z)=1-5/2z-1-3/2z-2, then the system is ___________
a) Minimum phase
b) Maximum phase
c) Mixed phase
d) None of the mentioned
Answer: Mixed phase

5. An IIR system with system function H(z)=B(z)A(z) is called a mixed phase if ___________
a) All poles and zeros are inside the unit circle
b) All zeros are outside the unit circle
c) All poles are outside the unit circle
d) Some, but not all of the zeros are outside the unit circle
Answer: Some, but not all of the zeros are outside the unit circle

6. What is the inverse of the system with impulse response h(n)=(1/2)nu(n)?
a) δ(n)+1/2 δ(n-1)
b) δ(n)-1/2 δ(n-1)
c) δ(n)-1/2 δ(n+1)
d) δ(n)+1/2 δ(n+1)
Answer: δ(n)-1/2 δ(n-1)

7. What is the inverse of the system with impulse response h(n)=δ(n)-1/2δ(n-1)?
a) (1/2)nu(n)
b) -(1/2)nu(-n-1)
c) (1/2)nu(n) & -(1/2)nu(-n-1)
d) None of the mentioned
Answer: (1/2)nu(n) & -(1/2)nu(-n-1)

8. A causal system produces the output sequence y(n)={1,0.7} when excited by the input sequence x(n)={1,-0.7,0.1}, then what is the impulse response of the system function?
a) [3(0.5)n+4(0.2)n]u(n)
b) [4(0.5)n-3(0.2)n]u(n)
c) [4(0.5)n+3(0.2)n]u(n)
d) None of the mentioned
Answer: [4(0.5)n-3(0.2)n]u(n)

9. If h(n) is the impulse response of an LTI system T and h1(n) is the impulse response of the inverse system T-1, then which of the following is true?
a) [h(n)*h1(n)].x(n)=x(n)
b) [h(n).h1(n)].x(n)=x(n)
c) [h(n)*h1(n)]*x(n)=x(n)
d) [h(n).h1(n)]*x(n)=x(n)
Answer: [h(n)*h1(n)]*x(n)=x(n)

10. What is the causal inverse of the FIR system with impulse response h(n)=δ(n)-aδ(n-1)?
a) δ(n)-aδ(n-1)
b) δ(n)+aδ(n-1)
c) a-n
d) an
Answer: an

11. If a system is said to be invertible, then?
a) One-to-one correspondence between its input and output signals
b) One-to-many correspondence between its input and output signals
c) Many-to-one correspondence between its input and output signals
d) None of the mentioned
Answer: One-to-one correspondence between its input and output signals