Lti Systems Continuous And Discrete – GATE ECE Signals And SystemsPractice Questions & PYQs

Consider the discrete-time system below with input $x[n]$ and output $y[n]$ . In the figure, $h_1[n]$ and $h_2[n]$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\delta[n]$ is the unit impulse, and $b > 0$ . Assuming $h_2[n] \ne \delta[n]$ , the overall system (denoted by the dashed box) is _______.

A causal and stable LTI system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$ . A signal $x(0.5 t)$ is applied to another causal and stable LTI system with impulse response $h(0.5 t)$ . The resulting output is ______

For a causal discrete-time LTI system with transfer function $H(z)=\frac{2 z^{2}+3}{\left(z+\frac{1}{3}\right)\left(z-\frac{1}{3}\right)}$ which of the following statements is/are true?

Consider a system with input $x(t)$ and output $y(t)=x\left(e^{t}\right)$ . The system is

Let $x(t)=10 \cos (10.5 \mathrm{Wt})$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 W t$ . The output of the system is

Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$ . If $X(t)$ is input to an LTI system with impulse response $e^{-t} u(t)$ . The average power of the system output is ___ $\mathrm{W}$ . (Rounded off to two decimal place).

The outputs of four systems $(S_1,S_2,S_3,S_4)$ corresponding to the input signal $\sin (t)$ , for all time $t$ , are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?

Let $x_1(t)=e^{-t}u(t)$ and $x_2(t)=u(t)-u(t-2)$ , where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_1(t)$ and $x_2(t)$ , then $\lim_{t\rightarrow \infty }y(t)=$ _________ (rounded off to one decimal place).

For a unit step input u[n], a discrete-time $\text{LTI}$ system produces an output signal $\left ( 2\delta \left[ n+1 \right] +\delta \left[ n \right]+\delta \left[ n-1 \right]\right )$ . Let $y[n]$ be the output of the system for an input $\left ( \left ( \dfrac{1}{2} \right )^n u\left[ n \right]\right )$ . The value of $y[0]$ is ______

The output y[n] of a discrete-time system for an input x[n] is

. The unit impulse response of the system is

Which one of the following pole-zero corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below? $y[n]=\sum_{k=0}^{3}(-1)^k x[n-k]$

Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $h_{1}(t)=2\delta (t+2)-3\delta (t+1)$ $h_{2}(t)=\delta(t-2)$ If the input x(t) is a unit step signal, then the energy of y(t) is ____________.

Two discrete-time signals x[n] and h[n] are both non-zero 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 _________.

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

The impulse response of an LTI system can be obtained by

The result of the convolution $x(-t)*\delta (-t-t_{o})$ is

Consider a discrete-time signal

If y[n] is the convolution of x[n] with itself, the value of y[4] is _____.

Two systems with impulse responses $h_{1}\left ( t \right )$ and $h_{2}\left ( t \right )$ are connected in cascade. Then the overall impulse response of the cascaded system is given by

Let y[n] denote 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] = 1/2, then g[1] equals

A system is defined by its impulse response $h(n) =2^{n} u(n - 2)$ . The system is