61. The z-transform of a system is $$H\left( z \right) = {z \over {z - 0.2}}.$$ If the ROC is |z| < 0.2, then the impulse response of the system is
62. The Dirac-delta function δ(t) is defined as
63. Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is
64. The response of an initially relaxed linear constant parameter network to a unit impulse applied at t = 0 is 4e-2tu(t). The response of this network to a unit step function will be
65. Consider the signal x(t) = cos(6πt) + sin(8πt), where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(2t + 5) is
66. The impulse response h[n] of a linear time invariant system is given as
$$h\left[ n \right] = \left\{ {\matrix{
{ - 2\sqrt 2 ,} \cr
{4\sqrt 2 ,} \cr
{0,} \cr
} } \right.\matrix{
{n = 1, - 1} \cr
{n = 2, - 2} \cr
{{\rm{otherwise}}} \cr
} $$
If the input to the above system is the sequence $${e^{{{j\pi n} \over 4}}},$$ the output is
$$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} \cr {4\sqrt 2 ,} \cr {0,} \cr } } \right.\matrix{ {n = 1, - 1} \cr {n = 2, - 2} \cr {{\rm{otherwise}}} \cr } $$
If the input to the above system is the sequence $${e^{{{j\pi n} \over 4}}},$$ the output is
67. If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of f(t) are respectively
68. A causal LTI system is described by the difference equation
2y[n] = αy[n - 2] - 2x|n| - βx[n - 1].
The system is stable only if
2y[n] = αy[n - 2] - 2x|n| - βx[n - 1].
The system is stable only if
69. The function f(t) has the Fourier transform f(ω)
The Fourier transform of
$$g\left( t \right) = \left( {\int\limits_{ - \infty }^\infty {g\left( t \right){e^{ - j\omega }}dt} } \right)$$ is
The Fourier transform of
$$g\left( t \right) = \left( {\int\limits_{ - \infty }^\infty {g\left( t \right){e^{ - j\omega }}dt} } \right)$$ is
70. The z-transform of a signal is given by $$C\left( z \right) = {1 \over 4}{{{z^{ - 1}}\left( {1 - {z^{ - 4}}} \right)} \over {{{\left( {1 - {z^{ - 1}}} \right)}^2}}}.$$ Its final value is
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