Signal Processing MCQ Questions & Answers

41

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system :

A) $$\frac{{{d^3}y}}{{d{t^3}}} + {a_1}\frac{{{d^2}y}}{{d{t^2}}} + {a_2}\frac{{dy}}{{dt}} + {a_3}y$$ $$ = {b_3}u + {b_2}\frac{{du}}{{dt}} + {b_1}\frac{{{d^2}u}}{{d{t^2}}}$$ (with initial rest conditions) B) $$y\left( t \right) = \int\limits_0^t {{e^{\alpha \left( {t - \tau } \right)}}} \beta u\left( \tau \right)d\tau $$ C) y = au + b, b ≠ 0 D) y = au

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Answer & Solution

Answer: Option C

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42

The z-transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - K} \right)} $$ is

A) $${z \over {z - {a^T}}}$$ B) $${z \over {z + {a^T}}}$$ C) $${z \over {z - {a^{ - T}}}}$$ D) $${z \over {z + {a^{ - T}}}}$$

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Answer & Solution

Answer: Option C

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43

The impulse response and the excitation function of a linear time invariant causal system are shown in figure (a) and (b) respectively. The output of the system at t = 2 sec is equal to
Signal Processing mcq question image

A) 0 B) $$\frac{1}{2}$$ C) $$\frac{3}{2}$$ D) 1

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Answer & Solution

Answer: Option B

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44

One period (0, T) each of two periodic waveforms W₁ and W₂ are shown in the figure. The magnitudes of the nth Fourier series coefficients of W₁ and W₂, for n ≥ 1, n is odd, are respectively proportional to
Signal Processing mcq question image

A) |n|^-3 and |n|^-2 B) |n|^-1 and |n|^-3 C) |n|^-1 and |n|^-2 D) |n|^-4 and |n|^-2

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Answer & Solution

Answer: Option C

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45

The Fourier Transform of the signal $$x\left( t \right) = {e^{ - 3{t^2}}}$$ is of the following form, where A and B are constants

A) $$A{e^{ - B{f^2}}}$$ B) $$A{e^{ - B{t^2}}}$$ C) $$A + B{\left| f \right|^2}$$ D) $$A{e^{ - Bf}}$$

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Answer & Solution

Answer: Option B

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46

The signal x(t) is described by
$$x\left( t \right) = \left\{ {\matrix{ {1\,{\rm{for}}} & { - 1 \le t \le + 1} \cr {0,} & {{\rm{otherwise}}} \cr } } \right.$$
Two of the angular frequencies at which its Fourier transform becomes zero are

A) π, 2π B) 0.5π, 1.5π C) 0, π D) 2π, 2.5π

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Answer & Solution

Answer: Option A

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47

The trigonometric Fourier series of an even function does not have the

A) Dc term B) Cosine terms C) Sine terms D) Odd harmonic terms

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Answer & Solution

Answer: Option C

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48

The impulse response of a system is h(t) = tu(t). For an input u(t - 1), the output is

A) $${{{t^2}} \over 2}u\left( t \right)$$ B) $${{t\left( {t - 1} \right)} \over 2}u\left( {t - 1} \right)$$ C) $${{{{\left( {t - 1} \right)}^2}} \over 2}u\left( {t - 1} \right)$$ D) $${{{t^2} - 1} \over 2}u\left( {t - 1} \right)$$

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Answer & Solution

Answer: Option C

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49

The unit impulse response of a linear time invariant system is the unit step function u(t). For t > 0, the response of the system to an excitation e^-at u(t), a > 0 will be

A) ae^-at B) $$\left( {{1 \over a}} \right)\left( {1 - {e^{ - at}}} \right)$$ C) a(1 - e^-at) D) 1 - e^-at

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Answer & Solution

Answer: Option C

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50

A signal x(n) = sin(ω₀n + f) is the input to a linear time-invariant system having a frequency response H(e^jω). If ihe output of the system Ax(n - n₀), then the most general form of ∠H(e^jω) will be

A) -n₀ω₀ + β for any arbitrary real β B) -n₀ω₀ + 2πk for any arbitrary integer k C) n₀ω₀ + 2πk for any arbitrary integer k D) $$ - {n_0}{\omega _0}\phi $$

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Answer & Solution

Answer: Option B

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Signal Processing MCQ Questions & Answers | ECE