Signal Processing MCQ

Test your knowledge with important Signal Processing MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Signal Processing MCQs at Bissoy

• The region of convergence of the z-transform of a unit step function is
  ক

  |z| > 1

  খ

  |z|

  গ

  (Real part of z) > 0

  ঘ

  (Real part of z)
• For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f + 2) is given by
  ক

  $${1 \over 2}x\left( {{t \over 2}{e^{j3\pi t}}} \right)$$

  খ

  $${1 \over 2}x\left( {{t \over 2}} \right){e^{ - {{j4\pi t} \over 3}}}$$

  গ

  3x(3t)e^-j4πt

  ঘ

  x(3t + 2)
• An FIR system is described by the system function<br>$$H\left( z \right) = 1 + \frac{7}{2}{z^{ - 1}} + \frac{3}{z}{z^{ - 2}}$$<br>The system is
  ক

  Maximum phase

  খ

  Minimum phase

  গ

  Mixed phase

  ঘ

  Zero phase
• The impulse response h(t) of a linear time-invariant continuous time system is described by h(t) = exp(αt)u(t) + exp(βt)u(-t), where u(t) denotes the unit step function, and α and β are real constants. This system is stable if
  ক

  α is positive and β is positive

  খ

  α is negative and β is negative

  গ

  α is positive and β is negative

  ঘ

  α is negative and β is positive
• Match the following and choose the correct combination.<br>
  ক

  <table class="table-style-1"> <tr> <td><strong>Group I</strong></td> <td><strong>Group II</strong></td> </tr> <tr> <td>E. Continuous and aperiodic signal</td> <td>1. Fourier representation is continuous and aperiodic.</td> </tr> <tr> <td>F. Continuous and periodic signal</td> <td>2. Fourier representation is discrete and aperiodic.</td> </tr> <tr> <td>G. Discrete and aperiodic signal</td> <td>3. Fourier representation is continuous and periodic.</td> </tr> <tr> <td>H. Discrete and periodic signal</td> <td>4. Fourier representation is discrete and periodic.</td> </tr></table> E-3, F-2, G-4, H-1

  খ

  E-1, F-3, G-2, H-4

  গ

  E-1, F-2, G-3, H-4

  ঘ

  E-2, F-1, G-4, H-3
• An excitation is applied to a system at t = land its response is zero for -∞
  ক

  Non-causal system

  খ

  Stable system

  গ

  Causal system

  ঘ

  Unstable system
• The Fourier transform of a voltage signal x(t) is X(f). The unit of |X(f)| is
  ক

  Volt

  খ

  Volt-sec

  গ

  Volt/sec

  ঘ

  Volt²
• {a(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence<br>$$y\left( n \right) = \frac{1}{N}\sum\limits_{r = 0}^{N - 1} {x\left( r \right)} x\left( {n + r} \right)$$      is
  ক

  $${\left| {X\left( k \right)} \right|^2}$$

  খ

  $$\frac{1}{2}\sum\limits_{r = 0}^{N - 1} {X\left( r \right)X'\left( {k + r} \right)} $$

  গ

  $$\frac{1}{2}\sum\limits_{r = 0}^{N - 1} {X\left( r \right)X\left( {k + r} \right)} $$

  ঘ

  0
• The bilateral Laplace transform of a function<br>$$f\left( t \right) = \left\{ {\matrix{ {1,} &amp; {{\rm{if}}\,a \le t \le b} \cr 0 &amp; {{\rm{otherwise}}} \cr } } \right.$$     is
  ক

  $${{a - b} \over s}$$

  খ

  $${{{e^z}\left( {a - b} \right)} \over s}$$

  গ

  $${{{e^{ - as}} - {e^{ - bs}}} \over s}$$

  ঘ

  $${{{e^{ - \left( {a - b} \right)}}} \over s}$$
• If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
  ক

  E

  খ

  $${E \over 2}$$

  গ

  2E

  ঘ

  4E
• Let δ(t) denote the delta function. The value of the integral $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)} \cos \left( {{{3t} \over 2}} \right)dt$$     is
  ক

  1

  খ

  -1

  গ

  0

  ঘ

  $${\pi \over 2}$$
• The ROC of z-transform of the discrete time sequence<br>$$x\left( n \right) = {\left( {{1 \over 3}} \right)^n}u\left( n \right) - {\left( {{1 \over 2}} \right)^n}u\left( { - n - 1} \right)$$       is
  ক

  [ <p><span>A. $${1 \over 3} <p><span>B. $$\left| z \right| &gt; {1 \over 2}$$

  খ

  $$\left| z \right|

  গ

  $$2
• The pole-zero pattern of a certain filter is shown in figure. The filter must be of the following type<br><img src="/images/question-image/electronics-and-communications-engineering/signal-processing/1681542537-the-pole-zero-pattern-of-a-certain.jpg" title="Signal Processing mcq question image" alt="Signal Processing mcq question image">
  ক

  Low-pass

  খ

  High-pass

  গ

  All-pass

  ঘ

  Band-pass
• A linear phase channel with phase delay T_p and group delay T_g must have
  ক

  T_p = T_g = constant

  খ

  $${{\rm{T}}_p}\,\alpha \,f\,{\rm{and}}\,{T_g} \propto f$$

  গ

  T_p = constant and T_g α f

  ঘ

  T_p α f and t_g = constant (f denotes frequency)
• Consider the differential equation $${{dx} \over {dt}} = 10 - 0.2x$$     with initial conduction x(0) = 1. The response x(t) for t &gt; 0 is
  ক

  2 - e^-0.2t

  খ

  2 - e^-0.2t

  গ

  50 - 49e^-0.2t

  ঘ

  50 - 49e^0.2t
• A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where<br>$$g\left( t \right) = \sum\limits_{k = - \infty }^\infty {{{\left( { - 1} \right)}^k}\delta \left( {t - 0.5 \times {{10}^{ - 4}}k} \right)} $$<br>The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be
  ক

  δ(t)

  খ

  m(t)

  গ

  0

  ঘ

  m(t) δ(t)
• A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$    To make this system causal it needs to be cascaded with another LTI system having a transfer function H₁(s). A correct choice for H₁(s) among the following options is
  ক

  s + 3

  খ

  s - 2

  গ

  s - 6

  ঘ

  s + 1
• Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is
  ক

  $${1 \over 5}{e^{3t}}u\left( { - t} \right) + {1 \over 5}{e^{ - 2t}}u\left( { - t} \right)$$

  খ

  $$ - {1 \over 5}{e^{3t}}u\left( { - t} \right) + {1 \over 5}{e^{ - 2t}}u\left( { - t} \right)$$

  গ

  $${1 \over 5}{e^{3t}}u\left( { - t} \right) - {1 \over 5}{e^{ - 2t}}u\left( t \right)$$

  ঘ

  $$ - {1 \over 5}{e^{3t}}u\left( { - t} \right) - {1 \over 5}{e^{ - 2t}}u\left( t \right)$$
• Specify the filter type if its voltage transfer function H(s) is given by<br>$$H\left( s \right) = {{K\left( {{s^2} + 1\omega _0^2} \right)} \over {{s^2} + \left( {{{{\omega _0}} \over Q}} \right)s + \omega _0^2}}$$
  ক

  All pass filter

  খ

  Low pass filter

  গ

  Band pass filter

  ঘ

  Notch filter
• If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$     then its final value is
  ক

  -1

  খ

  0

  গ

  1

  ঘ

  Unbounded
• The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$   is
  ক

  2e^-t - e^-3t

  খ

  2e^-t + e^-3t

  গ

  e^-t - 2e^-3t

  ঘ

  e^-t + 2e^-3t
• The final value theorem is used to find the
  ক

  Steady state value of the system output

  খ

  Initial value of the system output

  গ

  Transient behaviour of the system output

  ঘ

  None of these
• For a periodic signal<br>$$v\left( t \right) = 30\sin 100t + 10\cos 300t + 6\sin \left( {500t + {\pi \over 4}} \right),$$<br>the fundamental frequency in rad/s is
  ক

  100

  খ

  300

  গ

  500

  ঘ

  1500
• The first five points of the 8-point DFT of a real valued sequence are 5, 1 - j3, 0, 3 - j4 and 3 + j4. The last two points of the DFT are respectively
  ক

  0, 1 - j3

  খ

  0, 1 + j3

  গ

  1 + j3, 5

  ঘ

  1 - j3, 5
• The transfer function of a zero-order-hold system is
  ক

  $$\left( {\frac{1}{s}} \right)\left( {1 + {e^{ - sT}}} \right)$$

  খ

  $$\left( {\frac{1}{s}} \right)\left( {1 - {e^{ - sT}}} \right)$$

  গ

  $$1 - \left( {\frac{1}{s}} \right){e^{ - sT}}$$

  ঘ

  $$1 + \left( {\frac{1}{s}} \right){e^{ - sT}}$$
• A discrete-time all-pass system has two of its poles at 0.25
  ক

  [ <p><span>A. It has two more poles at 0.5 <p><span>B. It is stable only when the impulse response is two-sided

  খ

  It has constant phase response over all frequencies

  গ

  It has constant phase response over the entire z-plane
• Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$   is
  ক

  sF(s) - f(0)

  খ

  $${1 \over s}F\left( s \right)$$

  গ

  $$\int\limits_0^s {F\left( \tau \right)} d\tau $$

  ঘ

  $${1 \over s}\left$$
• The amplitude spectrum of a Gaussian pulse is
  ক

  Uniform

  খ

  A sine function

  গ

  Gaussian

  ঘ

  An impulse function
• Let h(t) denote the impulse response of a causal system with transfer function $${1 \over {s + 1}}.$$  Consider the following three statements:<br>S₁ : The system is stable.<br>S₂ : $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$  independent of t for t &gt; 0.<br>S₃ : A non-causal system with the same transfer function is stable.<br>For the above system,
  ক

  Only S₁ and S₂ are true

  খ

  Only S₂ and S₃ are true

  গ

  Only S₁ and S₃ are true

  ঘ

  S₁, S₂ and S₃ are true
• For an all-pass system $$H\left( z \right) = \frac{{\left( {{z^{ - 1}} - b} \right)}}{{\left( {1 - a{z^{ - 1}}} \right)}},$$     where | H(e^-jω) | = 1, for all ω. If Re(a) ≠ 0, lm(a) ≠ 0, then b equals
  ক

  a

  খ

  a^∗

  গ

  $$\frac{1}{{{a^ * }}}$$

  ঘ

  $$\frac{1}{a}$$