Important 2 marks Questions with Answers of Linear Time Invariant-Continuous Time Systems

Important 2 Mark Questions with Answers

UNIT 3: LINEAR TIME INVARIANT-CONTINUOUS TIME SYSTEMS

1. Define impulse response of a continuous time system.

Impulse response is the output produced by the system when input is applied to the system. Impulse response is denoted by h(t).

Impulse response is obtained by taking inverse Fourier transform (or) Inverse Laplace transform of transfer function.

2. Write does the input-output relation of LTI system in time and frequency domain.

In time domain : y(t) = y(t) * x(t)

3. Find the impulse response of the given system. y(t) = x(t – t₀)

Take Laplace transform of given equation.

Taking inverse Laplace transform of (1)

h(t) = δ(t-t₀)

4. Define transfer function in CT systems.

Transfer function relates the transforms of input and output.

5. What are the three elementary operations in block diagram representation of continuous time system.

The three elementary operations in block diagram representation of continuous time system are,

6. Find the transfer function of LTI system described the differential equation.

Taking Fourier transform of given differential equation.

7. What is the impulse response of two LTI systems connected in parallel?

If two systems are connected in parallel with their inputs x₁(t), x₂(t)  and their impulse response h₁(t) and h₂(t) then their overall impulse response is given as

h(t) = h₁(t) + h₂(t).

8. What is meant by impulse response of any system?

When the input x(t) is applied to the system, then the output (response) of the system to the input is known as impulse response.

The impulse response is used to study the various properties such as system stability, dynamicity, causality etc.

9. Find the impulse response of the system given by 

10. What is the condition for LTI system to be stable?

An LTI system is stable if its impulse response is absolutely integral.

An LTI system is stable if the ROC of its system transfer function includes

Re(s) = 0 (jω of S plane).

11. List the properties of convolution integral. (Nov - 2014).

(1) Commutative property

y(t) = x(t) * h(t) = h(t) * x(t)

(2) Associative property

[x(t) * h₁(t)] * h₂(t) = x(t) * [h₁(t) * h₂(t)]

(3) Distributive property of convolution

x(t) * h₁(t) + x(t) * h₂(t) = x(t) * {h₁(t) + h₂(t)}

12) State the significance of impulse response (Nov - 2014)

Impulse response is used to analyze the properties of a system such as dynamicity, equality and stability. Impulse response is a response of impulse δ(t) to any system.

13) Find the transfer function for the system described by the difference equation  (Apr/May 2008)

Take fourier transform

14) State the condition for LTI system to be causal and stable.

For a LTI system to be causal,

Causality: h(t) = 0 for t < 0

This condition shows that an impulse response of a causal system is also causal. Stability:

A LIT system is stable if, Stability: 

This condition show that the BIBO stable system has absolutely integrable impulse response.

15) Differentiate between natural response and forced response. (Nov/Dec: 2015)

i. In natural response only initial conditions are considered and input is zero.

ii. The forced response of the system is obtained only for input, with zero initial conditions.

16) Check whether the causal system with transfer function H(s) = 1/S-2 is stable. (Dec-13)

The pole lies at s = 2. Since the pole of causal system does not lie on left side of jω axis, the system is not stable.

17) What are the basic steps involved in convolution integrals?

Folding : One of the signal is first folded at t = 0.

Shifting : The folded signal is shifted right (or) left depending upon time at which output is to be calculated.

Multiplication: The shifted signal is multiplied with other signal.

Integtation : The multiplied signals are integrated to get convolution output.

18) What is the impulse response of an identity system? (May 08)

For an identity system.

Thus identity system has impulse response h(t) = δ(t)

19. A LTI system is characterized by th following differential equation  Find the frequency response of the system.

Taking fourier transform of given differential equation.

20) Write the N^th order differential equation.

The N^th order differential equation can be written as

21) Define the frequency response of the CT system. [Nov-11]

The response of a CT system to a complex sinusoidal signal gives the frequency response of the CT system.

Here, H(jΩ) is the frequency response of the CT system

22) Check the causality of the system with impulse response h(t) = e^-t u(t). [Nov-12]

For an LTI-CT system to be causal, h(t) = 0 for t < 0.

Here, h(t) = e^-t u(t) = 0 for t < 0. Hence, causal system

23) Draw the block diagram of the LTI system  [Nov-14] (R13)

24) What is u(t-2) * δ(t-1)? [Nov-15] (R13)

25) Give the differential equation representation of a system . Find the frequency response H(jΩ) [Nov-15] (R13)

26) Define Convolution integral of CT systems.

The convolution integral gives the output or response of a CT system which is the convolution of the input sequence [x(t)] & Impulse response [h(t)] sequence.

27) Find the differential eqn relating the i/p & o/p of a CT s/m rep'd by  [May-14]

Given:

28) Find whether the following system whose impulse response given is causal & stable. h(t) = e^-2t u(t-1) [May-16](R13)

(i) Since h(t) = 0 for t < 0, the given system is causal.

29) Realize the block diagram representing the system H(s) = 

Divide Numerator & Denominator by s,.