The energy of the signal $x\left(t\right)=\frac{\mathrm{sin}\left(4\pi t\right)}{4\pi t}$ is ________
Consider the function $g\left(t\right)={e}^{-t}\mathrm{sin}\left(2\pi t\right)u\left(t\right)$ where $u\left(t\right)$ is the unit step function. The area under $g\left(t\right)$ is _____.
The Fourier transform of a signal h(t) is $H\left(j\omega \right)=\left(2\mathrm{cos}\omega \right)\left(\mathrm{sin}2\omega \right)/\omega .$The value of h(0) is
Consider a system whose input x and output y are related by the equation
$\style{font-size:18px}{y\left(t\right)=\int\limits_{-\infty}^\infty x\left(t-\tau\right)h\left(2\tau\right)\operatorname{d}\tau}$
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.
The signal x(t) is described by
$x\left(t\right)=\left\{\begin{array}{ll}1& for-1\le t\le +1\\ 0& otherwise\end{array}\right.$
Two of the angular frequencies at which its Fourier transform becomes zero are
The impulse response h(t) of a 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 of this system to the sinusoidal input x (t) = 2cos (2t) for all time t, is
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 5-point sequence x[n] is given as
x[-3] = 1, x[-2] = 1, x[-1] = 0, x[0] = 5, x[1] = 1.
Let $X\left({e}^{j\omega}\right)$ denote the discrete-time Fourier transform of x[n]. The value of $\int\limits_{-\pi}^\pi X\left(e^{j\omega}\right)d\omega$ is