Consider the discrete-time system below with input  and output . In the figure,  and  denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also,  is the unit impulse, and .

Assuming , 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(0.5t). The resulting output is_________.

Consider a system with input  and output . The system is

 Let  and , where  denotes the unit step function.

If  denotes the convolution of  and , then  ________(rounded off to one decimal place).

The outputs of four systems , and  corresponding to the input signal , for all time , are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time. invariant)?

The output  of a discrete-time system for an input  is

The unit impulse response of the system is

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as  

Which one of the following statements is true about the system?

Consider the following statements for continuous-time linear time invariant (LTI) systems.          

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.

II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.  

Which one among the following is correct?

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  

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 _____________ .

The input x(t) and the output y(t) of a continuous-time system are related as

The system is  

Consider the parallel combination of two LTI systems shown in the figure.  

The implulse responses of the systems are

If the input x(t) is a unit step signal, then the energy of y (t) is _______________j

The result of the convolution  is

A continuous linear time-invariant filter has an impulse response h(t) described by

. When a constant input of value 5 is applied to this filter, the steady state output is ________.

Consider a discrete-time signal. If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

The impulse response of a continuous time system is given by . The value of the step response at t = 2 is

A system is defined by its impulse response . The system is  

Consider a system whose input x and output y are related by the equation

,

Where h(t) is shown in the graph

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.

Causal: The system is causal

LP: The system is low pass

LTI: The system is linear and time-invariant.        

The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?

A discrete time linear shift-invariant system has an impulse response h[n] with , , , and zero otherwise. The system is given an input sequence x[n] with  and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2, and P3 with system relations R1, R2, R3, R4. 

A system with input x[n] and output y[n] is given as . The system is:

Which of the following can be impulse response of a causal system?

The impulse response h[n] of a linear time-invariant system is given by

Where u[n] is the unit step sequence. The above system is

The impulse response h[n] of a linear time invariant system is given as         

If the input to the above system is the sequence, then the output is

Let P be linearly, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship,  

Where x(n) is the input and y(n) is the output. The above system has the properties

Convolution of x (t + 5) with impulse function is equal to

The impulse response functions of four linear systems  are given respectively by

Where U(t) is the unit step function. Which of these systems is time invariant, causal and stable?

A system with an input x(t) and output y(t) is described by the relation: . This system is

Let u(t) be the step function. Which of the waveforms in figures given in the options (a) – (d) corresponds to the convolution of  with

?

Match the followings

In the case of a linear time invariant system

(1) Poles in the right half plane implies

(2) Impulse response zero for  implies

(a) Exponential decay of output
(b) System is causal
(c) No stored energy in the system
(d) System is unstable

Let h(t) be the impulse response of a linear time-invariant system. Then the response of the system for any input u(t) is

An excitation is applied to a system at  and its response is zero for . Such a system is