Signals and Sys...

The signal x(t) = A cos(ωt + φ) is:

What is the total energy of the rectangular pulse shown in figure below?

For a finite support signal x[n] = r[n] (u[n] – u[n – 11]) where r[n] is the discrete-time ramp function, the energy of x[n] is

Which of the following systems are linear time-invariant and causal systems.

The z-transform of a sequence x[n] is given as x(z) = 3 + 4z – 6z^-1 + 2z^-2

The value of \(\mathop \sum \limits_{n = 0}^\infty n{\left( {\frac{1}{2}} \right)^n}\) is _________.

The sampling of a function f(t) = sin(2πf₀t) starts from zero-crossing. The signal can be detected, if sampling time T is:

What is the power and energy of the unit step sequence u(n) respectively?

The DTFT of a signal f(n) = {a, b, c, d} is F(ω). The inverse DTFT of F(ω - π) is:

The discrete Fourier series representation for the following sequence:

For a periodic signal v(t) = 30 sin100t + 10 cos300t + 6 sin(500t + π/4), the fundamental frequency in rad/s is

If a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal to:

Consider the sequence: x[n] = [- 4 - j5, 1 + j2, 4], the conjugate anti-symmetric part of the sequence is:

Which of the following statements is false.

The Fourier series coefficients of a periodic signal x(t), with fundamental frequency \({\omega _0} = \frac{\pi }{4}\) are \({X_1} = X_{ - 1}^* = j,\;{X_5} = X_{ - 5}^* = 2\) and the rest are zero. Suppose x(t) is the input to a band-pass filter with the following magnitude and phase responses.

\(H\left( {j\omega } \right) = \left\{ {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}{1,\;\;\pi \le \omega \le 1.5\pi }\\{1,\;\; - 1.5\pi \le \omega \le - \pi }\end{array}}\\{0,\;\;otherwise\;\;\;\;\;\;\;\;\;\;\;\;}\end{array}} \right.\)

∠H(jω) = -ω

Let y(t) be the output of the filter and the Fourier series of x(t) in the trigonometric form

\(x\left( t \right) = \mathop \sum \limits_{k = 0}^\infty {X_k}\cos \left( {k{\omega _0}t + \angle {X_k}} \right)\)

x(t) and the steady state response of y(t) are

Given the transform pair below. Determine the time signal y(t) and choose correct option.

Given the transform pair below. Determine the time signal y(t) and choose correct option.

Given the transform pair below. Determine the time signal y(t) and choose correct option.

The percentage of the total energy dissipated by a 1 Ω resistor in the frequency band 0 < ω < 10 rad/s when the voltage across it is v(t) = e^-2t u(t) is __________

Consider the following difference equation:

y[n] + 3y[n – 1] + 2y[n – 2] = 2x[n] – x[n – 1]

If y[-1] = 0, y[-2] = 1, x[n] = u[n], then y[n] can be represented as

A causal LTI system is described by the difference equation

2 y[n] = α y[n - 2] – 2 x[n] + β x[n - 1]

The system is stable only if

Determine the bilateral laplace transform and choose correct option

y(t) = δ(t + 1)

For a given periodic sequence x (n) = {1, 1, 0, 0} with period N = 4, the Fourier coefficient is denoted by c_k. The Value of c₃* is: