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The given mathematical representation belongs to:

y(t) = x(t - T)

This question was previously asked in
DFCCIL Executive S&T 29 Sept 2021 Official Paper
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  1. time multiplication
  2. time shifting
  3. time scaling
  4. time reversal

Answer (Detailed Solution Below)

Option 2 : time shifting
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Detailed Solution

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Time-shifting property: When a signal is shifted in time domain it is said to be delayed or advanced based on whether the signal is shifted to the right or left.

For example:

F9 Neha B 5-10-2020 Swati D7

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Q2.Which type of property is shown by the following function. L{K f(t)} = K F(s)
Q3.Let x1(t) = e-tu(t) and x2(t) = u(t) - u(t - 2), where u(⋅) denotes the unit step function. If y(t) denotes the convolution of x1(t) and x2(t), then \(\displaystyle \lim_{t\rightarrow\infty}y(t)=\) __________ (rounded off to one decimal place).
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Q6.If x(t) ↔ X(f) denotes a Fourier transform (FT) pair, \(\Pi \left(\dfrac{t}{T}\right)\) denotes a rectangular pulse of width T and '⋆' denotes the convolution operation, then the FT of the signal \(x(t)=\Pi \left(\dfrac{t}{T}\right) * \Pi \left(\dfrac{t}{T}\right)\) is
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Q10.Consider the following transfer functions: 1. \(\frac{1}{{j\omega + 1}}\) 2. \(\frac{1}{{{{\left( {j\omega + 1} \right)}^2}}}\)  3. \(\frac{1}{{\left( {j\omega + 1} \right)\left( {j\omega + 2} \right)}}\)  The transfer functions which have a linear phase are:

More Fourier Transform Questions

Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q4.Which one of the following is the correct relation ? (a > 0) 
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Q6.In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics I. Continuous, aperiodic a. Continuous, aperiodic II. Continuous, periodic b. Continuous, periodic III. Discrete, aperiodic c. Discrete, aperiodic IV. Discrete, periodic d. Discrete, periodic
Q7.The Fourier transform 𝑋(𝜔) of \(\rm x(t)=e^{-t^2}\) is Note: \(\rm \int_{-\infty}^{\infty}e^{-y^2}dy=\sqrt{\pi}\)
Q8.Let 𝑚(𝑡) be a strictly band-limited signal with bandwidth 𝐵 and energy 𝐸. Assuming 𝜔0 = 10𝐵, the energy in the signal 𝑚(𝑡) cos 𝜔0𝑡 is 
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Q10.Which symmetry does the Fourier transform of a real valued time signal contain?
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More Signals and Systems Questions

Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.What type of distortion occurs if a signal that contains frequency components up to 15 kHz is sampled using 20 kHz?
Q4.Which one of the following systems described by the following input-output relations is time invariant ? 
Q5.The equation for voltage waveform v(t) shown below is (where u(t) is unit step input) :
Q6.A continuous-time signal x(t) is defined as : \(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\) The energy of signal x(t) is : 
Q7.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q8.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q9.Which one of the following is the correct relation ? (a > 0) 
Q10.What is the formula of finding the final value of any time varying function f(t)?
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