11. Laplace transforms of the functions tu(t) and u(t)sin(t) are respectively
12. If $$x\left[ n \right] = {\left( {{1 \over 3}} \right)^{\left| n \right|}} - {\left( {{1 \over 2}} \right)^n}u\left[ n \right],$$ then the region of convergence (ROC) of its z-transform in the z-plane will be
13. A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cutoff frequency 800 Hz. The output signal has the frequency
14. Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
15. A Hilbert transformer is a
16. The trigonometric Fourier series of a periodic time function can have only
17. The Fourier transform of a signal
h(t) is $$H\left( {j\omega } \right) = {{\left( {2\cos \omega } \right)\left( {\sin \omega } \right)} \over \omega }$$
The value of h(0) is
h(t) is $$H\left( {j\omega } \right) = {{\left( {2\cos \omega } \right)\left( {\sin \omega } \right)} \over \omega }$$
The value of h(0) is
18. The output y(t) of a linear time invariant system is related to its input x(t) by the following equation:
y(t) = 0.5x(t - td + T) + x(t - td) + 0.5x(t - td -T).
The filter transfer function H(ω) of such a system is given by
y(t) = 0.5x(t - td + T) + x(t - td) + 0.5x(t - td -T).
The filter transfer function H(ω) of such a system is given by
19. Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
20. Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[I] is shown in the figure. Let $${W_6} = \exp \left( { - \frac{{j2\pi }}{6}} \right).$$ In the figure, what should be the values of the coefficients a1, a2, a3 in terms of W6 so that X[I] is obtained correctly?
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