Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 2141005 Signals And Systems Previous Question Paper

Enrolment No.___________

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE - SEMESTER? IV EXAMINATION ? SUMMER 2020**

**Subject Code: 2141005**

**Date:02/11/2020**

**Subject Name: SIGNALS AND SYSTEMS**

**Time: 10:30 AM TO 01:00 PM**

**Total Marks: 70**

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**Marks**

**Q.1 (a)**Based upon nature and characteristics in the time domain,

**03**

classify signals broadly. In each of the broad domains enlist

signals further classification.

**(b)**Sketch each of the following signals.

**04**

(i)

x[n] = u[n] - u[n - 5]

(ii)

x(t) = u(t+4) . u(-t +4)

**(c)**Classify following systems as : Causal or non-causal; Linear

**07**

or nonlinear and Time invariant or time variant

y(n) = log10

*x*(

*n*)

y(n)= n

*x*(n) +

*x*(n+2)

**Q.2 (a)**State and prove Linearity property of LTI systems using Laplace

**03**

transform.

**(b)**For LTI system, if input sequence is

*x*(n) and impulse response

**04**

is defined as h(n), derive equation for discrete time convolution

sum y(n).

**(c)**Consider a causal LTI system with impulse response

**07**

(

*h t*)

4

*e*

*tu*(

*t*). Find the output of the system for an input

*t*

*x t*

( )

*e*

.

3

**OR**

**(c)**

Solve the following difference equation

**07**

*y*(

*n*) 2

*y*(

*n*)

1

*x*(

*n*)

1

With

*x*( )

*n*

( )

*n*

*u*( )

*n*and initial condition y(-1)=1

3

**Q.3 (a)**Enlist dirichelts conditions for existence of Fourier transform.

**03**

**(b)**Find discrete time linear convolution of following two sequences

**04**

using matrices method.

*x*(

*n*) 2 (

*n*)

1 3 (

*n*) (

*n*)

1 2 (

*n*)

2

*h*(

*n*) 2 (

*n*)

1 3 (

*n*)

2 4 (

*n*)

3

**(c)**Compute the Fourier transform for the signal

*x*(t) in following

**07**

Figure:01

1

Figure:01

**OR**

**Q.3 (a)**Explain distributive property of LTI systems with suitable

**03**

figures.

**(b)**An LTI system has impulse response given by h(n)={2,1,2,1} .

**04**

Find its response to input

*x*(n)= {1,-2,4}.

**(c)**Compute the Fourier transform for the signal

*x*(t) in following

**07**

Figure: 02.

Figure:02

**Q.4 (a)**Prove that for causal sequences, the ROC of Z transform is

**03**

exterior of a circle.

**(b)**Find the Fourier transform of cosine wave cos

*w t*. Draw its

**04**

0

magnitude spectrum.

**(c)**State and prove (a) Differentiation in time domain and (b) time

**07**

shifting properties of LTI systems using Fourier transform.

**OR**

**Q.4 (a)**Explain with suitable mathematical equations, relation between

**03**

Laplace Transform and Fourier Transform,

**(b)**Using properties of Z transform, compute Z transform for

**04**

following signals.

x(n)= u(-n)

x(n)= u(-n-2)

**(c)**Find

fourier transforms of unit impluse function. Define clearly

**07**

Signam function (sgn(t)) and with its help find FT of unit step

function.

**Q.5 (a)**Find inverse Z transform of

**03**

1

*z*

*X*(

*z*)

;

*RoC z*1

3 4 1

2

*z*

*z*

**(b)**Using Z transform, find the convolution of the sequences

**04**

*x*( )

*n*

};

4

,

3

,

2

,

1

{

*x*( )

*n*

}

1

,

1

,

1

{

1

2

**(c)**Determine steady state (forced) response for the system with

**07**

1

impulse

response

(

*h*)

*n*

( )

*n*

*u*( )

*n*

for

the

input

2

*x*(

*n*) [cos(

*n*

)]

*u*(

*n*) .

**OR**

**Q.5 (a)**Find inverse Z transform of

**03**

2

3

2

1

2

3

*X*(

*z*) 2

*z*

*z*

*z*3 2

*z*4

*z*

*z*

**(b)**Write the properties of ROC of X(z).

**04**

**(c)**An LTI system is described by the difference equation

**07**

9

1

*y*( )

*n*

*y*(

*n*)

1

*y*(

*n*)

2

*x*( )

*n*3

*x*(

*n*)

1

4

2

Specify the ROC of H(z) and determine h(n) for the following

conditions,

(i)

The system is stable

(ii)

The system is causal

3

This post was last modified on 04 March 2021