Consider a discrete-time linear time-invariant (LTI) system , where

Let

where  is the discrete-time unit impulse function. For an input signal , the output  is

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

Let continuous-time signals  and  be

Consider the convolution . Then  is

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system . The output is observed to be the continuous-time unit step signal . Which one of the following statements is true?

Suppose signal  is obtained by the time-reversal of signal , i.e., . Which one of the following options is always true for the convolution of  and  ?

Which of the following statement(s) is/are true?

For the signals  shown in the figure,  is maximum at . Then  in seconds is __________ (Round off to the nearest integer).

Let a causal LTI system be governed by the following differential equation , where x(t) and y(t) are the input and output respectively. Its impulse response is

Consider the system as shown below

where . The system is

If the input x(t) and output y(t) of a system are related as y(t) = max (0, x(t)), then the system is

Two discrete-time linear time-invariant systems with impulse responses  and  are connected in cascade, where  is the Kronecker delta. The impulse response of the cascaded system is

Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:

The poles of this system are at

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t). Further, if |x(t)|*|h(t)| = z(t), which of the following statements is true?

Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:                

The Symbols, a and T, represent positive quantities, and  is the unit step function. Which one of the following impulse responses is not the output of a causal linear time-invariant system?

A continuous-time input signal x(t) is an Eigen function of an LTI system, if the output is

Consider the system with following input-output relation

Where x [n] is the input and y [n] is the output. The system is

Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore,

. The poles of H (z) are  for k = 1, 2, 3, 4.

The zeros of H(z) are all at z = 0. Let . The value of g[8] equals ___________________. (Given the answer up to three decimal places).  

Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where, x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

A cascade system having the impulse responses and is shown in the figure below, where symbol denotes the time origin.

The input sequence x(n) for which the cascade system produces an output sequence  is

Consider a continuous-time system with input x(t) and output y(t) given by

This system is

The impulse response g(t) of a system, G, is as shown in figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in figure (b)?

For linear time invariant systems, that are Bounded input Bounded output stable, which one of the following statements is TRUE?

The z – transform of a sequence  is given as. If y[n] is the first difference of x[n], then Y(z) is given by

x(t) is nonzero only for , and similarly, y(t) is nonzero only for . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?

An input signal  is sampled with a sampling frequency of 400Hz and applied to the system whose transfer function is represented by

Where, N represents the number of samples per cycle. The output y(n) of the system under steady state is

Two systems with impulse responses and  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  and g[n] is a casual sequence. If  and , then g[1] equals

The input x(t) and output y(t) of a system are related as. The system is

The response h(t) of a linear time invariant system to an impulse , under initially relaxed condition is . The response of this system for a unit step input u(t) is

The system represented by the input-output relationship

Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is  

A Linear Time Invariant system with an impulse response h(t) produces output y(t) when input x(t) is applied. When the input  is applied to a system with impulse response , the output will be

A cascade of 3 Linear Time Invariant systems is causal and unstable. From this, we conclude that

A signal is the input to a real Linear Time Invariant system.  Given K and φ are constants, the output of the system will be of the form  where

The Impulse response of a causal linear time variant system is given as h(t). Now consider the following two statements:                 

Statement (I):  Principle of superposition holds

Statement (II): h(t) = 0 for t < 0.

Which one of the following statements is correct'?

A system with input x(t) and output y(t) is defined by the input-output relation:                

The system will be

x[n] = 0; n <-1&n>0, x[-1]=-1, x[0]=2 is the input and y[n]=0; n<-1&n>2, y[-1]=–1=y[1], y[0]=3, y[2]=-2 is the output of a discrete time LTI system.  The system impulse response h[n] will be

A continuous time system is described by , where y(t) is the output and x(t) is the input. y(t) is bounded

Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is

s(t) is step response and h(t) is impulse response of a system. Its response y(t) for any input u(t) is given by

The impulse response of a network is  for  and zero otherwise. Find the impulse response of two such networks in cascade, neglecting loading effects.