A signal $x(n) = sin(\omega_on + \phi)$ is the input to a linear time invariant system having a frequency response $H(e^{j\omega})$. If the output of the system is $Axn - n_0$, then the most general form of $\angle H (e^{j\omega})$ will be

The unilateral Laplace transform of f(t) is $\dfrac{1}{s^2 + s +1}$. The unilateral Laplace transform of t f (t) is

In the following network, the switch is closed at t = 0^- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The samples x (n), n = (0, 1, 2....) are given by

In the following network, the switch is closed at t = 0^- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The expression and the region of convergence of the z −transform of the sampled signal are

The Laplace transform of i(t) is given by I(s) = $\dfrac{2}{s(1+s)}$ As t $\rightarrow$$\infty$, the value of i(t) tends to

The function x(t) is shown in figure. Even and odd parts of a unit-step function u(t) are respectively

Two systems H₁ (z) and H₂ (z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H₂ (z) is

The impulse response h (t) of linear time - invariant continuous time system is given by h (t) = exp (- 2t) u (t) , where u (t) denotes the unit step function.

The output of this system, to the sinusoidal input x (t) = 2 cos 2t for all time t, is

The z-transform X [z] of a sequence x[n] is given by x[z] =$\dfrac{0.5}{1-2z^{-1}}$. It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is

A system with transfer function H(z) has impulse response h(.), defined as h(2) = 1, h(3) = - 1 and h(k) = 0 otherwise. Consider the following statements.

S₁ : H(z) is a low-pass filter. S₂ : H(z) is an FIR filter.

Which of the following is correct?

A continuous time LTI system is described by ^{$\dfrac{d^2 y(t)}{dt^2} + 4 \dfrac{dy(t)}{dt} 3 y(t) = 2 \dfrac{dx(t)}{dt} + 4 \times (t)$}. Assuming zero initial condition, the response y(t) of the above system for the input x(t) = e^-2tu(t) is given by

The input and output of a continuous time system are respectively denoted by x (t) and y (t). Which of the following descriptions corresponds to a casual system?

Consider the function f(t) having Laplace transform F (s) = ^{$\dfrac{\omega_0}{s^2 + \omega^2_0}$} Re [s] > 0

The final value of f(t) would be

A system with input x [n] and output y [n] is given as y [n] = ^{$\left( sin\dfrac{5}{6} \pi n \right)$}x (n). The system is

The impulse response h (t) of linear time - invariant continuous time system is given by h (t) = exp (- 2t) u (t) , where u (t) denotes the unit step function.

The frequency response H $(\omega)$of this system in terms of angular frequency$(\omega)$, is given by H $(\omega)$ =

The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: $y(t) = 0.5 \times (t-t_d + T) + x(t-t_d) + 0.5 \times (t-t_d-T)$. The filter transfer function $H(\omega)$ of such a system is given by

Let x( t) and y( t) with Fourier transforms F (f) and Y( f) respectively be related as shown in Fig. Then Y( f) is

For an N-point FFT algorithm with N = 2m which one of the following statements is TRUE?

The 3-dB bandwidth of the low-pass signal e^-t u(t), where u(t) is the unit step function, is given by

A causal LTI system is described by the difference equation 2y[n] = $\alpha$y[n-2] -2x [n] + $\beta$x[n-1]
The system is stable only if