1. 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

2. 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 the Eigenfunction of the system.

A. True

B. False

3. 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. \(Ae^{j(\frac{nπ}{2}+26.6°)}\)

4. If the Eigenfunction 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 Eigenvalue of the system?

A. 3/2

B. -3/2

C. -2/3

D. 2/3

5. If h(n) is the real-valued impulse response sequence of an LTI system, then what is the imaginary part of the Fourier transform of the impulse response?

A. –\(\sum_{k=-∞}^∞ h(k) sinωk\)

B. \(\sum_{k=-∞}^∞ h(k) sinωk\)

C. –\(\sum_{k=-∞}^∞ h(k) cosωk\)

D. \(\sum_{k=-∞}^∞ h(k) cosωk\)

6. 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. –\(tan^{-1}\frac{H_I (ω)}{H_R (ω)}\)

7. 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|

8. 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

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. 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