Signals and Sys...

What will be the numerical value of the following integral?

\(\mathop \smallint \nolimits_{ - 1}^8 \left[ {\delta \left( {t + 3} \right) - 2\delta \left( {4t} \right)} \right]dt\)

The period of the given signal is:

\(x\left( n \right) = \sin \left( {\frac{{2\pi }}{5}n} \right) + 3\cos \left( {\frac{{2\pi }}{7}n} \right) + \cos \left( {\frac{{4\pi\;}}{{22}}n + \frac{\pi }{2}} \right)\)

Let f(t) be an even periodic signal with time period T and let y(t) be signal defined such that y(t) = f(t + T/4) then which of the following statement is true regarding Fourier series expansion of f(t) and y(t)

If \(x\left[ n \right] = cos\left[ {\frac{{3\pi n}}{4}} \right]\) and y[n] = sin (7πn). Then the value of \(\mathop \sum \limits_{n = - \infty }^{ + \infty } x\left[ n \right]y\left[ n \right]\) is__________.

DFT of a signal f(n) is known to be F(k) = {5, 3 + 6j, -1, 3 - 6j}

The DFT of the signal f(n - 3) will be:

For an LTI system with rational transfer function H(z), which of the following statements is/are true?

The energy of the signal x(t) is E/4 . If the signal is shrunk by a factor of 3 along the time scale the energy will now be

 Let X(z) be the z-transform of a discrete-time sequence \(x\left( n \right)={{\left( -\frac{1}{2} \right)}^{n}}u\left( n \right)\) 

Consider another signal y(n) and its z- transform Y(z), given as Y(z) = X (z³). The value of y(n) at n = 4 is ______.

The percentage of total energy in the signal \(f\left( t \right) = {e^{ - t}}u\left( t \right)\) contained in the frequency band |ω| < 5 rad/sec is ________.

Consider a periodic signal x(t) whose Fourier series coefficient is defined as below

\({c_n} = \left\{ {\begin{array}{*{20}{c}} {2\;\;\;\;\;\;\;,\;\;\;\;\;\;\;\;n = 0}\\ {j{{\left( {\frac{1}{2}} \right)}^{\left| n \right|}},\;\;\;otherwise} \end{array}} \right.\)

Which of the following conclusions is/are true?

An LTI system described by \(H\left( s \right) = \frac{1}{{{s^2} + 3s + 1}}\) Find the system response for the Input x(t) = 2cos (2t + 25°)