81. The input x(t) and the output y(t) of a continuous- time system are related as
$$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du} $$
The system is
$$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du} $$
The system is
82. The N-point DFT of a sequence x[n], 0 ≤ n ≤ N - 1 is given by
$$X\left[ K \right] = \frac{1}{{\sqrt N }}\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]} {e^{ - j\frac{{2\pi }}{N}nK}},0 \leqslant K \leqslant N - 1$$
Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT (DFT (x)) = x.
$$X\left[ K \right] = \frac{1}{{\sqrt N }}\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]} {e^{ - j\frac{{2\pi }}{N}nK}},0 \leqslant K \leqslant N - 1$$
Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT (DFT (x)) = x.
83. Convolution of x(t + 5) with impulse function δ(t - 7) is equal to
84. The Laplace transform of eαt cos (αt) is equal to
85. A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. y(t) + 5y(t) = u(t)
When y(0) = 1 and u(t) is a unit step function, y(t) is
When y(0) = 1 and u(t) is a unit step function, y(t) is
86. Consider the following statements for continuous-time linear time invariant (LTI) systems.
1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
87. The Fourier transform F{e-t u(t)} is equal to $${1 \over {1 + j2\pi f}}.$$ Therefore, $$F\left\{ {{1 \over {1 + j2\pi f}}} \right\}$$ is
88. A system with transfer function H(z) has impulse response h(n) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statements.
S1 : H(z) is a low-pass filter.
S2 : H(z) is an FIR filter.
Which of the following is correct?
S1 : H(z) is a low-pass filter.
S2 : H(z) is an FIR filter.
Which of the following is correct?
89. The Laplace transform of the causal periodic square wave of period T shown in the figure below is It
90. A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a
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