signal and system paper

1. Shroff s r rotary institute of chemical
technology
ankleshwar
Department of Electrical Engineering
Subject : SIGNALS AND SYSTEMS (2141005)
B.E. – Second Year – Fourth Semester
Term: JAN.-16 to May-16
Instructions:
[1]This set of Assignment-Tutorial consist the collection of questions of past GTU Question
papers.
[2] Attend all the questions as these are frequenly asked in GTU exam.
[3]Students should make a separate Chapter wise assignment [write in Notebook] to solve these
Questions.
[4]Students must solve these given set of Assignments by themselves only.
[5]Assessment of given assignment should be done regularly after completion of each chapter by
Students from the respective faculty members.
Contents :-[1] Detail Syllabus
[2] Chapter wise Assignment and Tutorial

2. Subject Code: 2141005
Subject Name: SIGNALS AND SYSTEMS
CHAPTER
NO.
SYLLABUS
1
Basic definitions, Classification of signals and systems. Signal operations and
properties. Basic continuous time signals, signal sampling and quantization,
discretization of continuous time signals, discrete time signals. Basic system
properties, Representation of digital signals. Case study of different signals form
communication and biomedical field
2
Impulse response characterization and convolution integral for CT- LTI system,
signal responses to CT-LTI system, properties of convolution, LTI system response
properties from impulse response. (*Review of Laplace transform with reference
to CT signals and systems.)
3
Impulse response characterization and convolution sum, Causal signal response to
DT-LTI systems. Properties of convolution summation, Impulse response of DT-
LTI system. DT-LTI system properties from Impulse response. System analysis
from difference equation model
4
Representation of periodic functions, Fourier series, Frequency spectrum of
aperiodic signals, Fourier Transform, Relation between Laplace Transform and
Fourier Transform and its properties. Introduction to DTFT and DFT
5
The z-Transform, Convergence of z-Transform, Basic z-Transform, Properties of
z-Transform, Inverse z-Transform and Solving difference equation using z-
Transform
Reference Books:
1. Signals and Systems by Alan V. Oppenheim, Alan S. Wilsky and Nawab, Prentice Hall
2. Signals and Systems by K. Gopalan, Cengage Learning (India Edition)
3. Signals and Systems by Michal J. Roberts and Govind Sharma, Tata Mc-Graw Hill
Publications
4. Signals and Systems by Simon Haykin and Bary Van Veen, Wiley- India Publications
5. Linear Systems and Signals by B.P.Lathi, Oxford University Press
6. Signal, Systems and Transforms by Charles L. Philips, J. M. Parr and E. A. Riskin, Pearson
Education
7. Digital Signal Processing Fundamentals and Applications by Li Tan, Elsevier, Academic Press

3. Chapter-1
Basic definitions, Classification of signals and systems. Signal operations and
properties. Basic continuous time signals, signal sampling and quantization,
discretization of continuous time signals, discrete time signals. Basic system
properties, Representation of digital signals. Case study of different signals form
communication and biomedical field
ATTEMPT ALL:
SR
NO.
QUESTION YEAR
MARK
S
1
For each of the following systems
i) y(t) = x(t-2) + x(2-t)
ii) y(n) = nx(n)
determine which of properties: “memoryless”, “time
invariant”, “linear”, “casual” holds and justify your answer.
June-15 07
2
Determine whether or not each of the following signals is
periodic. If the signal is periodic, determine its fundamental
period.
i) x(t) = [cos(2t- )]2
ii) x[n] = cos(n2
)
June-15 07
3
Define : Signal.
Find the fundamental periods (T for continuous-time signals, N
for discrete-time signals) of the following periodic signals.
1. x(t) = cos(13ᴫt) + 2sin(4ᴫt)
2. x[n] = ej7.351πn
Jan.-16 07
4
Define: System.
Determine whether the system y(t) = t x(t) is
1. Memoryless
2. Linear
3. Time invariant
4. Causal
5. BIBO stable. Justify your answers.
Jan.-16 07

4. Chapter-5
The z-Transform, Convergence of z-Transform, Basic z-Transform, Properties of z-
Transform, Inverse z-Transform and Solving difference equation using z-Transform
ATTEMPT ALL:
SR
NO.
QUESTION YEAR MARKS
1
Determine the z-transform for the following sequences. Sketch the
pole-zero plot and indicate the ROC. Indicate whether or not the
Fourier transform of the sequence exists.
i) δ[n+5]
ii) ( )n
u[3-n]
June-15 07
2
Using the long division method, determine the sequence that goes
with the following z-transforms:
and x[n] is right sided.
June-15 07
3
Using the Partial fraction method, determine the sequence that goes
with the following z-transforms:
and x[n] is absolutely summable.
June-15 07
4
List the properties of the region of convergence (ROC) for the z-
Transform.
June-15 07
5
Consider the signal
Determine the poles and ROC for X[z].
June-15 07
6
Find the Z transform of
1. δ(n)
2. u[n]
3. nan
u[n].
Jan.-16 07
7
Define: The Z transform.
State and prove Time shifting and Time reversal properties of Z
transform.
Jan.-16 07
8
Using power series expansion technique find the inverse Z
transform of
Jan.-16 07
9
Using the partial fraction expansion technique find the inverse Z
transform of
Jan.-16 07