71. The signal $$\cos \left( {10\pi t + \frac{\pi }{4}} \right)$$ is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $$\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi t}}} \right)\cos \left( {40\pi t - \frac{\pi }{2}} \right).$$ The filter output is
72. Let \[{x_1}\left( t \right) = \left\{ {\begin{array}{*{20}{c}}
6&{{\text{for }}0 < t < 4} \\
0&{{\text{otherwise}}}
\end{array}} \right.{\text{and }}{x_2}\left( t \right) = u\left( {t - 2} \right)\] and y(t) = x1(t) * x2(t), then the value of y(4) is
73. The impulse response of a causal, linear, time-invariant, continuous-time system is h(t). The output y(t) of the same system to an input x(t), where x(t) = 0 for t < -2, is
74. Given that h(t) = 10e-10u(t), and e(t) = sin10t.u(t), the Laplace transform of the signal $$f\left( t \right) = \int\limits_{\tau = 0}^t {h\left( {t - \tau } \right)e\left( \tau \right)d\tau } $$ is given by
75. Consider a 51 tap linear phase FIR filter operating at a sampling frequency of 10 kHz. The delay of this linear phase FIR is:
76. A digital filter has transfer function $$H\left( z \right) = \frac{{{z^2} + 1}}{{{z^2} + 0.81}}.$$ If the filter has to rejecta 50 Hz interference from the input, then the sampling frequency for the input signal should be:
77. A linear time invariant system has an impulse response e2t, for t > 0. If initial conditions are zero and the input is e3t, the output for t > 0 is
78. The z-transform of the discrete time signal x(n) = u(n)*u(n) with '*' being convolution is
79. If a linear time invariant system is excited by a true random single like white noise, the output of the linear system will have which of the following properties?
80. Given the 'Energy Spectrum Density, Sxx(f) of a sequence x(n)
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