Frequency Analysis of Signals and Systems topics include: Frequency analysis of discrete and continuous time signals, fourier transform properties, convolution and de-convolution concepts, inverse systems, LTI systems and discrete time signals.

While time-domain analysis shows how a signal changes over time, frequency-domain analysis shows how the signal's energy is distributed over a range of frequencies.

In signal processing, time–frequency analysis is a body of techniques and methods used for characterizing and manipulating signals whose statistics vary in time, such as transient signals.

Digital Signal Processing Practice Test: Frequency Analysis of Signals and Systems

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25 Questions

1. According to Parseval’s Theorem for non-periodic signal, \(\int_{-∞}^∞|x(t)|^2 dt\).

\(\int_{-∞}^∞|X^* (F)|^2 dt \) \(\int_{-∞}^∞ X(F).X^*(F) dt \) All of the mentioned\(\int_{-∞}^∞|X(F)|^2 dt \)

2. If x(n)=Ae^jωn 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?

H(ω)x(n)-H(ω)x(n)None of theseH(-ω)x(n)

3. What is the value of discrete time signal x(n) at n=0 whose Fourier transform is represented as below?

ωc.π-ωc/πnone of the mentionedωc/π

4. What is the equation of the Fourier series coefficient ck of an non-periodic signal?

\(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_{-\infty}^∞ x(t)e^{-j2πkF_0 t} dt\)

5. Which of the following relation is true if the signal x(n) is real?

None of theseX*(ω)=X(-ω)X*(ω)=X(ω)X*(ω)=-X(ω)

6. What is the inverse of the system with impulse response h(n)=δ(n)-1/2δ(n-1)?

(1/2)nu(n) & -(1/2)nu(-n-1)None of these(1/2)nu(n)-(1/2)nu(-n-1)

7. 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 H_R(ω) and H_I(ω)?

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

8. If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as ______________

None of theseHigh frequency signalMiddle frequency signalLow frequency signal

9. Which of the following represents the phase associated with the frequency component of discrete-time Fourier series(DTFS)?

none of the mentionedej2πkn/Nej2πknNe-j2πkn/N

10. If h_lp(n) denotes the impulse response of a low pass filter with frequency response H_lp(ω), then what is the frequency response of the high pass filter in terms of H_lp(ω)?

Hlp(ω+π)Hlp(ω-π)Hlp(ω-π/2)Hlp(ω+π/2)

11. If F₁ and F₂ are the lower and upper cutoff frequencies of a band pass signal, then what is the condition to be satisfied to call such a band pass signal as narrow band signal?

(F1-F2)⋙\(\frac{F_1+F_2}{2}\)(factor of 10 or more)(F1-F2)>\(\frac{F_1+F_2}{2}\)(factor of 3 or less)(F1-F2)<\(\frac{F_1+F_2}{2}\)(factor of 3 or less)(F1-F2)⋘\(\frac{F_1+F_2}{2}\)(factor of 10 or more)

12. What are the Fourier series coefficients for the signal x(n)=cosπn/3?

c0=c1=c2=c3=c4=c5=0c0=c1=c2=c3=c4=c5=1/2none of the mentionedc1=c2=c3=c4=0,c1=c5=1/2

13. 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)?

\(\frac{1}{(1-\frac{1}{2} e^{-jω})(1+\frac{1}{4} e^{-jω})}\) \(\frac{1}{(1-\frac{1}{2} e^{-jω})(1-\frac{1}{4} e^{-jω})}\) \(\frac{1}{(1+\frac{1}{2} e^{-jω})(1-\frac{1}{4} e^{-jω})}\) \(\frac{1}{(1+\frac{1}{2} e^{-jω})(1+\frac{1}{4} e^{-jω})}\)

14. A two pole low pass filter has a system function H(z)=\(\frac{b_0}{(1-pz^{-1})^2}\), What is the value of ‘b₀‘ such that the frequency response H(ω) satisfies the condition |H(π/4)|²=1/2 and H(0)=1?

0.360.320.460.38

15. 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?

1+a1-aanone of the mentioned

16. Which of the following condition is to be satisfied for the Fourier transform of a sequence to be equal as the Z-transform of the same sequence?

Can never be equal|z|>1|z|<1|z|=1

17. What is the Fourier series representation of a signal x(n) whose period is N?

\(\sum_{k=-\infty}^{\infty}|c_k|\) \(\sum_{k=-\infty}^0|c_k|^2\) \(\sum_{k=0}^{\infty}|c_k|^2\) \(\sum_{k=-\infty}^{\infty}|c_k|^2\)

18. Which filter has a magnitude frequency response as shown in the plot given below?

High pass FilterBand stop FilterBand pass FilterLow pass Filter

19. What is the magnitude of H(ω) for the three point moving average system whose output is given by y(n)=\(\frac{1}{3}[x(n+1)+x(n)+x(n-1)]\)?

|1-2cosω| \(\frac{1}{3}|1-2cosω|\) \(\frac{1}{3}|1+2cosω|\) |1+2cosω|

20. 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?

[h(n)*h1(n)]*x(n)=x(n)[h(n).h1(n)].x(n)=x(n)[h(n)*h1(n)].x(n)=x(n)[h(n).h1(n)]*x(n)=x(n)

21. Which of the following is the equation for the Fourier series coefficient?

\(\frac{1}{T_p} \int_{t_0}^∞ x(t)e^{-j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_{t_0}^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\) \(\frac{1}{T_p} \int_0^{t_0+T_p} x(t)e^{-j2πkF_0 t} dt\)

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

23. What is the energy of a discrete time signal in terms of X(ω)?

\(\frac{1}{2π} \int_0^π |X(ω)|^2 dω\) \(2π\int_{-π}^π |X(ω)|^2 dω\) \(\frac{1}{2π} \int_{-π}^π |X(ω)|^2 dω\) None of these

24. If the frequency response of an FIR system is given as H(z)=1-z^-1-6z^-2, then the system is ___________

Minimum phaseMixed phaseMaximum phaseNone of these

25. For a signal x(n) to exhibit even symmetry, it should satisfy the condition |X(-ω)|=| X(ω)|.

MaybeTrueDon't KnowFalse

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