Q1:

Steady state value of x(n) if

$x\left(z\right)=\frac{z\left(z+1\right)}{\left(z-1\right)\left(z^2-1.4z+0.48\right)}$

Q2:

Find initial value of x(s)=$\frac{4s+5}{2s+1}$

Q3:

Find Inverse Laplace transform of $x\left(s\right)=\log \left(\frac{s+5}{s+6}\right)$

Q4:

If the discrete time sequence is Given by x[n] = {1, 2, 3, 4} the x(e^jo) = ?

Q5:

If y”-6y'+5y= y(0) ; y(0)=1;y'(0)=-3 then y(t) is:-

Q6:

The sinusoidal signal $x(t)=5\mathrm{Cos}\left(200t+\frac{\pi }{6}\right)$is passed through a square Law device defined by the input relation $y(t)=x^2(t)$. The DC component in signal is?

Q7:

The complex exponential Fourier series representation of a signal f(t) over the interval (-∞ to ∞) is  $f(t)={\displaystyle \sum _{-\infty }^{\infty }\frac{3}{4+{(n\pi )}^2}}$$e^{jn\pi t}$ .What is the numerical value of A if during expansion one of its component is A $cos3\pi t.$

Q8:

An LTI system has impulse response $h\left(t\right)=e^{-2t}u(t)$and input to the system is $x(t)=\cos 2t.$The value of y(t) at t=0 is?

Q9:

Find inverse Fourier Transform of $x(\omega )=e^{-\left|\omega \right|}$

Q10:

For a periodic square wave, which one of the following statement is true?

Q11:

Fourier series of the waveform shown in the figure

Q12:

The discrete time Fourier series coefficient of the signal $x(n)=5cos\left(\frac{\pi }{2}n\right)$is?

Q13:

The discrete time Fourier series representation of the signal $x[n]={\displaystyle \sum _{-\infty }^{\infty }\delta (n-5K)}$is?

Q14:

A discrete time signal is given by $x[n]={\mathrm{Cos}}^2\left[\frac{\pi }{8}n\right]$. If the complex Fourier series coefficient of the signal are represented as $c_K$. Then value of $c_{15}$ is ?

Q15:

The function shown in the following figure is repeated at equal interval of time for $-\infty <t<\infty$. The value

Of the amplitude of the 5^th harmonic is:

Q16:

For a periodic signal $V(t)=30sin100t+10cos300t+6sin\left(500t+\frac{\pi }{4}\right)$.calculate fundamental frequency and time period?

Q17:

Two system with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascade system is given by

Q18:

The input x(t) and output y(t) of a system are related as $y(t)={\displaystyle \underset{-\infty }{\overset{t}{\int }}x(\tau )\cos (3\tau )d\tau .}$ The systems are

Q19:

Let y[n] denotes the convolution of h[n] and g[n], where h[n] = (1/2)ⁿ u[n] and g[n] is a causal sequence. if y[0] = 1 and y[1] = ½, then g[1] equals

Q20:

An input x(t)=e^–2t u(t)+$\delta$(t-6) is applied  to an LTI system with impulse response h(t)=u(t).

The output is