Two discrete time systems with impulse responses h₁[n] = $\delta$[n -1] and h₂[n] = $\delta$[n - 2] are connected in cascade. The overall impulse response of the cascaded system is

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1, 0, 2, 3} is

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) = 2$\delta$(n-3) where $\delta$(n) = $ \begin{cases} 1, n = 0 \\ 0, otherwise \end{cases}

$ The output at n = 4 is

The input x(t) and output y(t) of a system are related as y(t) = $ \oint_\infty x(\tau) cos(3 \tau) \ d\tau $the system is

A linear, time - invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4 and one simple zero at s = - 1. A unit step u (t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

For a signal x(t), the Fourier transform is X(f). Then the inverse Fourier transform of X(3f + 2) is given by

Consider the sequence| x[n] = [– 4 – j51 + j25]. The conjugate anti-symmetric part of the sequence is

The system under consideration is an RC low-pass filter (RC-LPF) with R = 1.0 k$\Omega$and C = 1.0 $\delta$F.

Let tg(f) be the group delay function of the given RC-LPF and f2 = 100 Hz. Then tg(f2) in ms, is

The power in the signal s(t) = 8 cos $\left( 20\pi t - \dfrac{\pi}{2} \right)$ + 4 sin $(15 \pi t)$ is

A 5-point sequence x (n) is given as X [–3] = 1, x [–2] = 1, x [–1] = 0, x [0] = 5, x [1] = 1. If x(^{$e^{j\omega}$}) denotes the discrete – time fourier transform of x [n], what is the value of ^{$\displaystyle \int_{-\pi}^\pi x(e^{j\omega})$$d\omega$}?

If the unit step response of a network is $(1 - e^{-\omega t})$, then its unit impulse response is

Choose the function $f(t); -\infty \lt 1 \lt +\infty$for which a Fourier series cannot be defined.

The system under consideration is an RC low-pass filter (RC-LPF) with R = 1.0 k$\Omega$and C = 1.0$\mu$F.

Let H(f) denote the frequency response of the RC-LPF. Let f1 be the highest frequency such that 0$\le$|f| $\le$f₁, $\dfrac{ | H(f_1) | }{H(0)}$$\ge$ 0.95. Then f₁ (in Hz) is

The trigonometric Fourier series for the waveform f(t) shown below contains

The impulse response h [n] of a linear time-invariant system is given by h[n]= u[n+3] + u [n-2)-2n[n-7] where u[n] is the unit step sequence. The above system is

If the region of convergence of x₁ [n] + x₂ [n] is ^{$\dfrac{1}{3} \lt |z| \lt \dfrac{2}{3}$}, then the region of convergence of x_n [n] - x₂ [n] includes

Let x(t) be the input to a linear, time-invariant system. The required output is 4x (t-2). The transfer function of the system should be

A function is given by f (t) = sin² t + cos 2t. Which of the following is true?

The differential equation 100$\dfrac{d^2 y}{dt^2}$- 20$\dfrac{dy}{dt}$ + y = x(t) describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

In the system shown below, x (t ) = (sin t)u (t). In steady-sate, the response y (t) will be