The value of $\int_{-\infty}^{+\infty}e^{-t}\delta\left(2t-2\right)\mathrm{dt}$ where $\delta \left(t\right)$ is the Dirac delta function, is
The function shown in the figure can be represented as
A discrete system is represented by the difference equation
$\left[\begin{array}{cc}{X}_{1}& \left(K+1\right)\\ {X}_{2}& \left(K+1\right)\end{array}\right]=\left[\begin{array}{cc}a& a-1\\ a+1& a\end{array}\right]\left[\begin{array}{c}{X}_{1}\left(K\right)\\ {X}_{2}\left(K\right)\end{array}\right]$
It has initial conditions X_{1}(0) = 1; X_{2}(0) = 0. The pole locations of the system for a = 1, are
An input signal x(t) 2 + 5sin(100πt) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by
$\frac{\mathrm{Y}\left(\mathrm{z}\right)}{\mathrm{X}\left(\mathrm{z}\right)}=\frac{1}{\mathrm{N}}\left(\frac{1-{\mathrm{Z}}^{-\mathrm{N}}}{1-{\mathrm{Z}}^{-1}}\right)$
where, N represents the number of samples per cycle. The output y(n) of the system under steady state is
A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) has a frequency of
A zero mean random signal is uniformly distributed between limits − a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is
Given a sequence x[n], to generate the sequence y[n] = x[3 − 4n], which one of the following procedures would be correct ?
The frequency spectrum of a signal is shown in the figure. If this signal is ideally sampled at intervals of 1 ms, then the frequency spectrum of the sampled signal will be
(A)
(B)
(C)
(D)
A signal is processed by a causal filter with transfer function G(s). For a distortion free output signal wave form, G(s) must
$G\left(s\right)=\alpha {z}^{-1}+\beta {z}^{-3}$ is a low pass digital filter with a phase characteristics same as that of the above question if