The Fourier transform of a real valued time signal has
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The RMS value of a rectangular wave of period T, having a value of +V for a duration, T1(< T) and -V for the duration, T - T1 = T2 equals
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A continuous time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period Ts. In which one of the following cases is the sampled signal periodic?
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The phase response of a passband waveform at the receiver is given by
where fc is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmittance to receiver is
where fc is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmittance to receiver is
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For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then
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A continuous time LTI system is described by
Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e-2tu(t) is given by
Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e-2tu(t) is given by
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A rectangular pulse train s(t) as shown in the figure is convolved with the signal cos2(4π × 103t). The convolved signal will be a
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The transfer function of a zero-order hold is
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The 3-dB bandwidth of the low-pass signal e-tu(t), where u(t) is the unit step function, is given by
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A system is described by the differential equation Let x(t) be a rectangular pulse given by
x\left( t \right) = \left\{ {\matrix{ {1,} & {0 < t < 2} \\ {0,} & {{\rm{otherwise}}} \\ } } \right.
Assuming that y(0) = 0 and at t = 0, the Laplace transform of y(t) is
x\left( t \right) = \left\{ {\matrix{ {1,} & {0 < t < 2} \\ {0,} & {{\rm{otherwise}}} \\ } } \right.
Assuming that y(0) = 0 and at t = 0, the Laplace transform of y(t) is
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A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz, and then passed through a low pass filter with a cut-off frequency of 8 kHz. The filter output
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If the signal with denoting the convolution operation, then x(t) is equal to
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A sequence x(n) with the z-transform X(z) = z4 + z2 - 2z + 2 - 3z-4 is applied as an input to a linear, time-invariant system with the impulse response h(n) = 2δ(n - 3) where
\delta \left( n \right) = \left\{ {\matrix{ {1,} & {n = 0} \\ {0,} & {{\rm{otherwise}}} \\ } } \right.
The output at n = 4 is
\delta \left( n \right) = \left\{ {\matrix{ {1,} & {n = 0} \\ {0,} & {{\rm{otherwise}}} \\ } } \right.
The output at n = 4 is
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The Laplace transform of i(t) is given by
As t → ∞, the value of i(t) tends to
As t → ∞, the value of i(t) tends to
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A real-valued signal x(t) limited to the frequency band is passed through a linear time invariant system whose frequency response is H\left( f \right) = \left\{ {\matrix{
{{e^{ - j4\pi f,}}} & {\left| f \right| \le {W \over 2}} \\
{0,} & {\left| f \right| > {W \over 2}} \\
} } \right.
The output of the system is
The output of the system is
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The signal x(t) = sin(14000πt), where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response H(t) as follows:
H\left( f \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{\left| f \right| \leqslant 12kHz} \\ {0,}&{\left| f \right| > 12kHz} \end{array}} \right.
What is the number of sinusoids in the output and their frequencies in kHz?
H\left( f \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{\left| f \right| \leqslant 12kHz} \\ {0,}&{\left| f \right| > 12kHz} \end{array}} \right.
What is the number of sinusoids in the output and their frequencies in kHz?
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A signal is the input to an LTI system with the transfer function
If Ck denote the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to
If Ck denote the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to
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Let and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is
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A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is
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The result of the convolution
x(- t) ∗ δ(- t - t0) is
x(- t) ∗ δ(- t - t0) is
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