AKT MEMORIAL COLLEGE OF ENGINEERING AND TECHNOLOGYNEELAMANGALAM, KALLAKURICHI 606 202

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

EC6303- SIGNALS AND SYSTEMS

QUESTION BANK

UNIT-III LINEAR TIME INVARIANT CONTINUOUS TIME SYSTEMS

PART A

1. Given x(t) = δ(t). Find X(s) and X(ω). AM-15 R-132. State the convolution integral. AM-15 R-13,AM-15, MJ-13,AM-11,AM-103. State the condition for the LTI system to be causal and stable. AM-15,MJ-13

4. Draw the block diagram of the LTI system described by dy (t)dx

+ y (t)=0.1x (t) . ND-14

R-135. Find y (n) = x (n-1)¿ δ (n-2). ND-14 R-136. List the properties of convolution integral. ND-147. State the significance of impulse response.ND-148. State the necessary and sufficient condition for an LTI continuous time system to be

causal. MJ-149. Find the differential equation relating the input and output a CT system represented

by H(jΩ) =4

( j Ω)2+8 j Ω+4. MJ-14

10. What are the three elementary operations in block diagram representation on CT system? ND-13,12

11. Check whether the causal system with transfer function H(s) = 1s−2 is stable.ND-13

12. Check the causality of the system with impulse response h(t) = e-t u(t). ND-1213. Determine the Laplace transform of the signal δ(t-5) and u(t-5). MJ-1214. Determine the convolution of the signals x[n] = {2, -1, 3, 2} and h(n) = {1, -1, 1,

1}.MJ-1215. Define state equation and state transition matrix. ND-1116. Determine the response of the system with impulse response h(t) = t u(t) for the

input x(t) = x(t). ND-1117. What is meant by impulse response of any system?AM-1118. Write down the convolution integral to find the output of the continuous time systems.

ND-1019. Write the Nth order differential equation.ND-10

20. What is impulse response of two LTI systems connected in parallel.AM-1021. What is the Laplace transform of the function x(t) = u(t) – u(t – 2)? ND-0922. What are the transfer functions of the following? ND-09

(a) An ideal integrator(b) An ideal delay of T seconds.

PART- B

1. (i) Solve the differential equation (D2+3D+2) y(t) = D x(t) using the input x(t) = 10 e-3t

and with initial condition y(0+) = 2 and y(0+) = 3. 10

(ii) Draw the block diagram representation for H(s) = 4 s+28s2+6 s+5

.6 AM-15 R-13

2. (i) For a LTI system with H(s) = s+5

s2+4 s+3 find the differential equation. Find

the System output y(t) to the output x (t) = e-2t u(t).10

(ii) Using graphical method convolve x (t) = e-2t u(t) with h(t) = u(t + 2). 6 AM-15 R-13

3. Find the output response of the system described by a differential equation

d2 y (t )d t2

+5 dy (t)dt

+ 6y (t) = x (t) when the input signal x (t) = cos t. The initial

conditions are dd y¿¿ = 1 ; y(0+) = 1. 16 AM-154. Discuss the various properties of Laplace transform. 16 AM-155. Find the overall impulse response of the following system.

Here h1(t) = e-2t u(t)

h2(t) = δ (t) – δ (t−1)

h3(t) = δ (t)Also find the output of the system for the input x(t) = u(t) using convolution integral. 16 ND-14 R-13

6. An LTI system is represented by d2

dt2y ( t )+4 d

dty (t )+4 y ( t )=x (t) with initial

conditions y(0) = 0 ; y’(0) = 1 ; Find the output of the system, when the input is x|t| = e-t u(t). 16 ND-14 R-13

7. Find the block diagram representation and state space representation of the system given by

d2 y (t )dt 3

+3d2 y (t )dt2

+5dy (t)dt

+6 y ( t )= d2 x (t )dt 2

+6dx (t)dt

+5 x ( t ) .16 ND-14

8. (i) Solve : d2 y (t )dt2

+4 dy (t)dt

+4 y ( t )=dx (t)dt

+x (t ) with y(0) = 9/4, y’(0) = 5 and

x(t)= e-3t u(t). 10

(ii)The frequency response of continuous LTI system is H(jΩ) = a− j Ωa+ j Ω with

a > 0. Find the impulse response of the system. 6 ND-149. Using convolution integral, determine the response of a CT LTI system y(t) given

input x(t) = e- t α u(t) and impulse response h(t) = e- tβ u(t), |α|<1 ,|β|< 1 .16 MJ-1410. Find the frequency response of the system shown below :16 MJ-14

11. (i) Define convolution integral and derive its equation. 8(ii) A stable LTI system is characterized by the differential equation

d2 y (t )dt2

+4 dy (t)dt

+3 y (t )=dx (t)dt

+2x (t ) Find the frequency response and

impulse response using Fourier Transform.8 ND-1312. (i) Draw direct form, cascade form and parallel form of a system with system

function. H(s) = 1

(s+1 )(s+2) .8

(ii) Determine the state variable description corresponding to the block diagram given below. 8 ND-13

13.