PYQs Based test 7: Signals & Systems

Which one of the following is an eigen function of the class of all continuous-time, linear, time invariant systems (u(t) denotes the unit-step function)?

Two discrete-time signals x[n] and h[n] are both non-zero only for n = 0,1,2, and are zero otherwise. It is given that

x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1

Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is ________.

A discrete-time signal x[n] = δ [n - 3] + 2δ [n - 5] has a z-transform X(z). If Y(z) = X(-z) is the z-transform of another signal y[n], then

Let the signal f(t) = 0 outside the interval [T₁, T₂], where T₁ and T₂ are finite. Furthermore, $\left|\mathrm{f}\left(\mathrm{t}\right)\right|<\infty$. The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is

A discrete-time signal x[n] = $x\left[n\right]=e^{j\left(\frac{5\pi }{3}\right)n}+e^{j\left(\frac{\pi }{4}\right)n}$ is down-sampled to the signal x${}_d$ [n] such that x${}_d$ [n] = x[4n]. The fundamental period of the down-sampled signal x${}_d$ [n] is __________.