A Hilbert transformer is a

Given f(t) = L^{–1 $\left[ \dfrac{3s+1}{s3 + 4s2 + (K-3)s} \right]$}. If ^{$\displaystyle lim_{x \rightarrow \theta}$}f(t) = 1, then the value of K is

{x (n)} is a real - valued periodic sequence with a period N. x (n) and X (k) form N - point Discrete Fourier Transform (DFT) pairs. The DFT Y (k) of the sequence y (n) = $\dfrac{1}{n} \displaystyle \sum_{r = 0} ^{N-1} x (r) \times (n+r)$is

Given that F (s) is the one-sided Laplace transform of f (t). What is the Laplace transform of ^{$\int_0^t f(\tau) d\tau$}?

Consider a system whose input x and output y are related by the equation y (t) = ^{$\displaystyle \int_{-\infty} ^\infty x(t - \tau) g(2\tau) d\tau$}, 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.

Let $x(n) = \left( \dfrac{1}{2} \right) ^ n u(n), \ y(n) = x^2(n)$ and $Y (e^{j\omega})$ be the Fourier transform of y(n)  Then $Y(e^{j0})$ is

If the Laplace transform of a signal y (t) is y(s) = $\dfrac{1}{s(s-1)}$, its final value is

The unit impulse response of a system is h (t) = e^-t , t$\ge$ 0 For this system, the steady-state value of the output for unit step input is equal to

The z-transform of a system is H(z) = $\dfrac{z}{z-0.2}$. If the ROC is |z| < 0.2, then the impulse response of the system is

Let (x) t be the input and (y) t be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R ||| |---|---| | Properties| Relations| | P1 : Linear but NOT time - invariant| R1 : y (t) = t² x (t)| | P2 : Time - invariant but NOT linear| R2 : y (t) = |t| x (t)| | P3 : Linear and time - invariant| R3 : y (t) = |x (t)|| | | R4 : y (t) = x (t - 5)|

The impulse response H [n] of a linear time invariant system is given as $h[n] = \begin{cases} -2\sqrt 2 & n=1, -1 \\ 4\sqrt 2 & n=2, -2 \\ 0 & otherwise \end{cases}

$ If the input to the above system is the sequence e^j$\pi$n/4, then the output is

The signal x (t) is described by x (t) =$ \begin{cases} 1 & for \ -1 \le t \le + 1 \\ 0 & otherwise \end{cases}

$ Two of the angular frequencies at which its Fourier transform becomes zero are

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship, Y(n) = $ \begin{cases} x(n), & n \ge 1 \\ 0 & n=0 \\ x(n+1), & n \le -1 \end{cases}

$ where x(n) is the input and y(n) is the output. The above system has the properties

An LTI system having transfer function $\dfrac{s^2 +1}{s^2 +2s + 1}$ and input x (t) = sin (t + 1) is in steady state. The output is sampled at a rate $\omega_s$rad/s to obtain the final output {x (k)}. Which of the following is true?

The frequency response of a linear, time-invariant system is given by H(f) = $\dfrac{5}{1 + j10\pi f}$ The step response of the system is

Match the following and choose the correct combination:

The Dirac delta function $\delta$ (t) is defined as