81. A unit impulse function δ(t) is defined by
1. δ(t) = 0 for all t except t = 0
2. $$\int_{ - \infty }^\infty {\delta \left( t \right)dt = 1} $$
The Fourier transform F(ω) of δ(t) is
1. δ(t) = 0 for all t except t = 0
2. $$\int_{ - \infty }^\infty {\delta \left( t \right)dt = 1} $$
The Fourier transform F(ω) of δ(t) is
82. Consider an LTI system subjected to a wide sense stationary input {x(n)}, which is a white noise sequence. The cross correlation Φxy[m] between input x(n) and output y(n) is:
Where Φxx[m] = $$\sigma _{\text{x}}^2\delta \left[ {\text{m}} \right]$$ and h[.] is impulse response
Where Φxx[m] = $$\sigma _{\text{x}}^2\delta \left[ {\text{m}} \right]$$ and h[.] is impulse response
83. If |H(ω)| = H(ω)H(-ω) then
84. Let x(n) be a real-valued sequence that is a sample sequence of a wide-sense stationary discrete-time random process. The power density of this signal is
85. Consider an impulse response h[n] = {-3, -1, 2, 1, 3}, system is . . . . . . . . phase and . . . . . . . . pass filter.
86. If the input x(t) = u(t) + u(t - 1) is applied to a LTI system whose impulse response is given by h(t) = δ(t), then the response of the system y(t) is
87. A system is defined by its impulse response h(n) = 5nu(n - 5). The system is
88. Let $$X\left( {{e^{j\omega }}} \right) = \sum\nolimits_{n = - \infty }^\infty {x\left[ n \right]{e^{ - j\omega n}}} $$ and $$x\left[ n \right] = \frac{1}{{2\pi }}\int\limits_{ - \pi }^\pi {X\left( {{e^{j\omega }}} \right){e^{j\omega n}}d\omega } .$$
If $$X\left( {{e^{j\omega }}} \right) = \frac{1}{{\left( {1 - 0.2{e^{ - j\omega }}} \right)\left( {1 - 0.1{e^{ - j\omega }}} \right)}},$$ what is x[n] in terms of unit discrete step function u(n)?
If $$X\left( {{e^{j\omega }}} \right) = \frac{1}{{\left( {1 - 0.2{e^{ - j\omega }}} \right)\left( {1 - 0.1{e^{ - j\omega }}} \right)}},$$ what is x[n] in terms of unit discrete step function u(n)?
89. Sampling theorem denoted as
90. Given $$\mathop y\limits^{..} \left( t \right) + 3\mathop y\limits^. \left( t \right) + 4y\left( t \right) = 2\mathop x\limits^{..} \left( t \right) + 7\mathop x\limits^. \left( t \right) + 8x\left( t \right)$$
Then H(s) is given by
Then H(s) is given by
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