LTI System Frequency Characteristics MCQ’s

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “LTI System Frequency Characteristics”.

1. An LTI system is characterized by its impulse response h(n)=(1/2)nu(n). What is the spectrum of the output signal when the system is excited by the signal x(n)=(1/4)nu(n)?
a) \frac{1}{(1-\frac{1}{2} e^{-jω})(1+\frac{1}{4} e^{-jω})}
b) \frac{1}{(1-\frac{1}{2} e^{-jω})(1-\frac{1}{4} e^{-jω})}
c) \frac{1}{(1+\frac{1}{2} e^{-jω})(1-\frac{1}{4} e^{-jω})}
d) \frac{1}{(1+\frac{1}{2} e^{-jω})(1+\frac{1}{4} e^{-jω})}

2. If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1, then what is the output of the system when input x(n)=5+12sin\frac{π}{2}n-20cos(πn+\frac{π}{4})?(Given a=0.9 and b=0.1)
a) 5+0.888sin(\frac{π}{2}n-420)-1.06cos(πn-\frac{π}{4})
b) 5+0.888sin(\frac{π}{2}n-420)+1.06cos(πn+\frac{π}{4})
c) 5+0.888sin(\frac{π}{2}n-420)-1.06cos(πn+\frac{π}{4})
d) 5+0.888sin(\frac{π}{2}n+420)-1.06cos(πn+\frac{π}{4})

3. If h(n) is the real valued impulse response sequence of an LTI system, then what is the imaginary part of Fourier transform of the impulse response?
a) –\sum_{k=-∞}^∞ h(k) sin⁡ωk
b) \sum_{k=-∞}^∞ h(k) sin⁡ωk
c) –\sum_{k=-∞}^∞ h(k) cos⁡ωk
d) \sum_{k=-∞}^∞ h(k) cos⁡ωk

4. If the system gives an output y(n)=H(ω)x(n) with x(n) = Aejωnas input signal, then x(n) is said to be Eigen function of the system.
a) True
b) False

5. If x(n)=Aejωn is the input of an LTI system and h(n) is the response of the system, then what is the output y(n) of the system?
a) H(-ω)x(n)
b) -H(ω)x(n)
c) H(ω)x(n)
d) None of the mentioned

6. What is the frequency response of the system described by the system function H(z)=\frac{1}{1-0.8z^{-1}}?
a) \frac{e^{jω}}{e^{jω}-0.8}
b) \frac{e^{jω}}{e^{jω}+0.8}
c) \frac{e^{-jω}}{e^{-jω}-0.8}
d) None of the mentioned

7. What is the response of the system with impulse response h(n)=(1/2)nu(n) and the input signal x(n)=10-5sinπn/2+20cosπn?
a) 20-\frac{10}{\sqrt{5}} sin(π/2n-26.60)+ \frac{40}{3}cosπn
b) 20-\frac{10}{\sqrt{5}} sin(π/2n-26.60)+ 40cosπn
c) 20-\frac{10}{\sqrt{5}} sin(π/2n+26.60)+ \frac{40}{3cosπn}
d) None of the mentioned

8. If the Eigen function of an LTI system is x(n)= Aejnπ and the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?
a) 3/2
b) -3/2
c) -2/3
d) 2/3

9. What is the magnitude of the frequency response of the system described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1?
a) \frac{|b|}{\sqrt{1+2acosω+a^2}}
b) \frac{|b|}{1-2acosω+a^2}
c) \frac{|b|}{1+2acosω+a^2}
d) \frac{|b|}{\sqrt{1-2acosω+a^2}}

10. What is the magnitude of H(ω) for the three point moving average system whose output is given by y(n)=\frac{1}{3}[x(n+1)+x(n)+x(n-1)]?
a) \frac{1}{3}|1-2cosω|
b) \frac{1}{3}|1+2cosω|
c) |1-2cosω|
d) |1+2cosω|

11. The output of the Linear time invariant system cannot contain the frequency components that are not contained in the input signal.
a) True
b) False

12. If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0 < a < 1, then what is the parameter ‘b’ so that the maximum value of |H(ω)| is unity?
a) a
b) 1-a
c) 1+a
d) none of the mentioned

13. What is the output sequence of the system with impulse response h(n)=(1/2)nu(n) when the input of the system is the complex exponential sequence x(n)=Aejnπ/2?
a) Ae^{j(\frac{nπ}{2}-26.6°)}
b) \frac{2}{\sqrt{5}} Ae^{j(\frac{nπ}{2}-26.6°)}
c) \frac{2}{\sqrt{5}} Ae^{j({nπ}{2}+26.6°)}
d) Ae^{j(\frac{nπ}{2}+26.6°)}

14. If h(n) is the real valued impulse response sequence of an LTI system, then what is the phase of H(ω) in terms of HR(ω) and HI(ω)?
a) tan^{-1}\frac{H_R (ω)}{H_I (ω)}
b) –tan^{-1}\frac{H_R (ω)}{H_I (ω)}
c) tan^{-1}\frac{H_I (ω)}{H_R (ω)}
d) –tan^{-1}\frac{H_I (ω)}{H_R (ω)}

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