This document is a past exam paper for an EEC-404 Signals and Systems course. It contains 3 sections with multiple choice and numerical problems related to signals and systems concepts. Section A contains 10 short answer questions testing definitions, properties and operations related to signals, systems, Laplace transforms, Z-transforms, Fourier transforms, convolution, and block diagrams. Section B contains 5 longer answer questions on properties, Fourier transforms, convolution, correlation and filter responses. Section C contains 5 multi-part problems involving plots, proofs, transforms, convolution, correlation and filter characteristics. The document provides an exam for students to test their understanding of key concepts across time, frequency and transform domains for continuous and discrete time signals and systems.

1. Divya Jyoti College of Engineering & Technology
Printed Pages:2 EEC-404
(Following Paper ID and Roll No. to be filled in your Answer Book)
PAPER ID : 0324 Roll No:
B.Tech.(ECE)
(Semester-IV)Theory Examination (2011 – 12)
SIGNALS AND SYSTEMS
Time: 3 Hours] [Total Marks : 100
Note: This question paper contain three sections. Attempt questions from each section as per directions.
Section-A
Attempt all part of this question. 2X10=20
1. (a) Define signal and system with suitable examples.
(b) Comment on the periodicity of discrete time signal cos3πn + sin8πn. Also find the
even and odd components of the above signal.
(c) Find the laplace transform of sin2t u(t).
(d) Determine inverse Z transform of az-1/(1- az-1)2 [assume |z|>a]
(e) Find the continuous time fourier transform of gate pulse of width 4.
(f) Find the discrete time fourier transform of x(n)={1,1,1,1,1}
(g) Find the convolution sum of x(n)={1,2,1} and h(n)={2,3,1}
(h) Find the convolution integral of x(t)=e-atu(t) and h(t)=e-btu(t).
(i) Represent the given transfer function with the help of block diagram.
H(s)=(s+1)(s+2)/(s+3)(s+4)
(j) Represent the given system function with the help of block diagram.
H(Z)=(1+Z-1)/(1+2Z-1)(1+3z-1)
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2. Divya Jyoti College of Engineering & Technology
Section-B
Attempt all part of this question. 6X5=30
2. (a) Write five properties of unit sample sequence.
(b) Write the properties of ROC of Laplace transform and Z transform.
(c) The discrete time fourier transform of the signal is given by
X(f)=[rect{50(f-0.25)}+rect{50(f+0.25)}]*comb(f). Here comb(x)=Σn=-∞δ(x-n). Find
the discrete time signal x(n).
(d) Prove the relationship between convolution and correlation and write the properties
of autocorrelation function.
(e) Calculate the impulse response, transfer function and step response of a first order
low pass filter.
Section-C
Attempt all questions. 10X5=50
3. Plot the magnitude of x(t)=ej2t + ej3t
Or
Comment on the frequency domain periodicity of discrete time exponential signal ejωn and
calculate it’s power.
4. Write and prove the convolution in time domain property of Laplace transform.
Or
State and prove the final value theorem of Z transform.
5. Obtain CTFT of u(t) and DTFT of u(n).
Or
Find the energy at the output of low pass filter with cut off frequency 1/T radian if
x(t)=e-t/Tu(t) is given as an input to the filter.
6. Find the convolution of x1(t) and x2(t) given below.
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3. Divya Jyoti College of Engineering & Technology
Or
Find the correlation between x1(t) and x2(t) given below.
7. Find the relationship between Bandwidth and Rise time of first order low pass filter.
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