The lengths of two discrete time sequences $x_1(n)$ and $x_2(n)$ are 5 and 7, respectively. The maximum length of a sequence $x_1(n) * x_2(n)$ is ______.

For a signal $x(t)$, the Fourier transform is $X(f)$. Then the inverse Fourier transform of $X(3f+2)$ is ______.

Two discrete time systems with impulse responses $h_1[n] = \delta[n-1]$ and $h_2[n] = \delta[n-2]$ are connected in cascade. The overall impulse response of the cascaded system is ______.

For a periodic signal $v(t) = 30\sin 100t + 10\cos 300t + 6\sin(500t + \pi/4)$ the fundamental frequency in rad/s is ______.

A discrete time system has impulse response $h[n] = 2^n u(n-4)$. Write 'Yes' if the system is stable or 'No' if the system is not stable. ______

The impulse response of a system is $h(t) = t u(t)$. For an input of $u(t-2)$ the output is ______.

The average power in the signal $s(t) = 10\cos(20\pi t - \pi/2) + 6\sin(15\pi t)$ is ______.

$\int_{-\infty}^{\infty} \delta(t) dt = ______.

The ROC of Laplace transform does not contain any ______.

Z-transform is used for ______ time signal.

Stability

Causality

Random signal

Time-variant system

Linear system

Delta function

Memoryless system

$x(3-t)$

$x(4t+1)$

$[x(t) + x(-t)] u(t)$

$[\delta(t+1) + \delta(t-1)] x(t)$

$x(t)x(t-5)$

$x(t)\delta(t-3)$

$x(2t-5)$

$x(t) = \delta(t-t_0)$

$x(t) = u(t-t_0)$

$x(t) = e^{-2t} [u(t) - u(t-5)]$

$x(t) = \sum_{k=0}^\infty \delta(t - kT)$

$x(t) = \delta(at+b)$, $a, b$ real constants

$x(t) = 1/t$

$x(t) = \sin t$

$x[n] = \sin(\pi^2 n)$

$x(t) = \cos t + \sin 3t$

$x[n] = \cos \frac{n}{4}$

$x[n] = \cos^2 \frac{\pi}{8} n$

$x(t) = \sin t + \sin 2t$

$x[n] = \sin(5\pi n)$

$x(t) = e^{-j3\pi/4}$

Even and odd symmetric signal

Initial and final value theorem of Laplace transform

Random and deterministic signals

Force voltage analogy