Signals and System 2024 — MAKAUT · EC-303 · Mid Sem PYQ with solutions

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Maulana Abul Kalam Azad University of Technology

Solutions

26 answers across 3 groups

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Group AVery Short Answer Type Question · answer any 10 · 1 mark each

  1. I

    In a ______ signal, we can define the value of the signal at any instant of time?

    aContinuousbDiscretecBoth a) and b)dNone of the aboveFree sample

    Answer: (a) Continuous

    Explanation

    A continuous-time signal is defined for all values of time tt.

  2. II

    The discrete time system, y(n)=x(n−3)−4x(n−10)y(n) = x(n-3) - 4x(n-10) is a,

    adynamic systembmemoryless systemctime varying systemdnone of the above
  3. III

    Fourier transform is applicable to

    aonly periodic signalsbonly aperiodic signalscboth periodic and aperiodic signalsdonly random signals
  4. IV

    The region of convergence of x/(1+2x+x2)x / (1+2x+x^2) is

  5. V

    The Nyquist theorem for sampling

      1. Relates the conditions in time domain and frequency domain
      1. Helps in quantization
      1. Limits the bandwidth requirement
      1. Gives the spectrum of the signal
    a1, 2 and 3 are correctb1 and 2 are correctc1 and 3 are correctdAll the four are correct
    Show answer to question V
  6. VI

    The system y(t)=2x(n+1)+x(1/n)y(t) = 2x(n+1) + x(1/n) is

    acausal systembnon-causal systemcpartly (a) and partly (b)dnone of these
  7. VII

    An LTI discrete time system is causal if and only if,

    ah(n) \neq 0 for n < 0bh(n) = 0 for n < 0ch(n) \neq \infty for n < 0dh(n) \neq 0 for n > 0
  8. VIII

    What is the ROC of z-transform of finite duration anti-causal sequence?

    az=0bz=\inftycEntire z-plane, except at z=0dEntire z-plane, except at z=\infty
  9. IX

    What is the one sided z-transform X(z) of the signal x(n)={5,7,0,1}x(n)=\{5,7,0,1\}

    az^2+2z+5+7z^{-1}+z^{-3}b5+7z+z^3cz^{-2}+2z^{-1}+5+7z+z^3d5+7z^{-1}+z^{-3}
  10. X

    What impact does increasing the sample size have on the sampling error?

    aIncreases the sampling errorbReduces the sampling errorcNo EffectdAll of the above
  11. XI

    The anti-causal sequences have components in the left hand sequences.

    aPositivebNegativecBoth a and bdNone of the above
  12. XII

    The Z-Transform X(z) of a discrete time signal x(n) is defined as _________

    a\sum_{n=-\infty}^{\infty} x(n)Z^nb\sum_{n=-\infty}^{\infty} x(n)Z^{-n}c\sum_{n=0}^{\infty} x(n)Z^ndNone of these

Group BShort Answer Type Question · answer any 3 · 5 marks each

  1. 2

    A continuous time signal is shown in fig. Find the following versions of the signal. Comment on the result.

    • a) x(t-2)
    • b) x(-t)
    • c) x(-t +2)

    [Figure: A continuous-time signal x(t) plotted against t. It is 0 for t < -3. It rises linearly from (-3, 0) to (-2, 2). It remains constant at 2 from t = -2 to t = -1. It falls linearly from (-1, 2) to (0, 0). It is 0 for t > 0.]

    Show answer to question 2
  2. 3

    Difference Between Continuous Time and Discrete Time Fourier Series. What is magnitude spectrum and phase spectrum.

  3. 4

    What is Negative Frequency? Show the relation between Fourier Coefficients of Trigonometric and Exponential form

  4. 5

    Obtain the transfer function of a system whose input is given by x(n)=[2δ(n+1)+3δ(n)−2δ(n−1)+δ(n−2)]x(n) = [2\delta(n+1) + 3\delta(n) - 2\delta(n-1) + \delta(n-2)] & output is given by y(n)=[δ(n+1)+2δ(n)−4δ(n−1)+δ(n−2)]y(n) = [\delta(n+1) + 2\delta(n) - 4\delta(n-1) + \delta(n-2)].

    Write the time shifting property of Z transform.

    Show answer to question 5
  5. 6

    Determine the Fourier Series of

    • (a)
      x(n)=2cos⁡3πnx(n) = 2 \cos \sqrt{3}\pi n
    • (b)
      x(n)=4cos⁡πn2x(n) = 4 \cos \frac{\pi n}{2}
    Show answer to question 6

Group CLong Answer Type Question · answer any 3 · 15 marks each

  1. 7

    Find the Fourier series expansion of the Signal and draw the Fourier spectrum

    [Figure: A continuous-time periodic signal x(t) plotted against t. The waveform is a sawtooth wave. In the fundamental period from t = -\pi to t = \pi, the signal is a straight line passing through the origin, rising from (-\pi, -\pi) to (\pi, \pi). The period is T = 2\pi.]

    Show answer to question 7
  2. 8(a)

    Determine the Laplace Transform of the following signals

    [Figure: A continuous-time signal x(t) plotted against t. It is a single period of a square wave starting at t=0. It has an amplitude of A from t=0 to t=T/2, and an amplitude of -A from t=T/2 to t=T. It is 0 elsewhere.]

    Show answer to question 8(a)8 marks
  3. 8(b)

    [Figure: A continuous-time signal x(t) plotted against t. It is a single rectangular pulse of amplitude 1 starting at t=0 and ending at t=a. It is 0 elsewhere.]

    7 marks
  4. 9

    Determine the Fourier series representation of the following discrete time signal and sketch the frequency spectrum.

    x(n)={…,1,2,−1,1↑,2,−1,1,… }x(n) = \{\dots, 1, 2, -1, \underset{\uparrow}{1}, 2, -1, 1, \dots\}

    Show answer to question 9
  5. 10(a)

    Consider the elementary signal u(t). The signal u(t+4) is obtained by shifting u(t) to the left by 4 units

    5 marks
  6. 10(b)

    The signal u(-t+4) is obtained by reversing u(t) and then shifting u(-t) to the right by 4 units

    5 marks
  7. 10(c)

    The signal x(t) is obtained by multiplying u(t+4) and u(-t+4)

    5 marks
  8. 11(a)

    Test the Stability of the system y(t)=cos⁡(x(t))y(t) = \cos(x(t))

    7 marks
  9. 11(b)

    Prove ∫−∞+∞∣h(t)∣dt<∞\int_{-\infty}^{+\infty} |h(t)| dt < \infty, for stability of an LTI system.

    8 marks

About this paper

The MAKAUT Signals and System (EC-303) 2024 Mid Sem previous year question paper, set in semester 3. Download the verified PDF or read it online, then check your answers against the worked solutions above.

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What is the subject code for Signals and System?

EC-303 is the MAKAUT subject code for Signals and System.

Which exam is this Signals and System question paper from?

The MAKAUT 2024 Mid Sem exam, semester 3. A student shared it, and it was checked before publishing.

Which branches is this Signals and System paper for?

B.Tech Electronics and Communication Engineering.

Where can I find more EC-303 question papers?

On the Signals and System subject page, which collects every year's papers along with notes and the syllabus.

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