COntents: Signals & Systems, Classification of Continuous and Discrete Time signals, Standard Continuous and Discrete Time Signals Block Diagram Representation of System, Properties of System Linear Time Invariant Systems (LTI) Convolution, Properties of Convolution, Performing Convolution Differential and Difference Equation Representation of LTI Systems Fourier Series, Dirichlit Condition, Determination of Fourier Coefficeints, Wave Symmetry, Exponential Form of Fourier Series Fourier Transform, Discrete Time Fourier Transform Laplace Transform, Inverse Laplace Transform, Properties of Laplace Transform Z-Transform, Properties of Z-Transform, Inverse Z- Transform Text Book Signal & Systems (2nd Edition) By A. V. Oppenheim, A. S. Willsky & S. H. Nawa Signal & Systems By Prentice Hall Reference Book Signal & Systems (2nd Edition) By S. Haykin & B.V. Veen Signals & Systems By Smarajit Gosh

1. Signals & Systems
Lecture#01

2. COURSE CONTENT
 Signals& Systems,ClassificationofContinuousandDiscreteTimesignals, Standard
ContinuousandDiscreteTimeSignals
 BlockDiagramRepresentationofSystem,PropertiesofSystem
 LinearTimeInvariantSystems(LTI)
 Convolution,Propertiesof Convolution,PerformingConvolution
 DifferentialandDifferenceEquationRepresentationofLTI Systems
 FourierSeries,DirichlitCondition,DeterminationofFourier Coefficeints,WaveSymmetry,
ExponentialForm ofFourierSeries
 FourierTransform,DiscreteTimeFourierTransform
 LaplaceTransform,Inverse LaplaceTransform,PropertiesofLaplaceTransform
 Z-Transform,PropertiesofZ-Transform,Inverse Z-Transform

3. BOOKS
Text Book
Signal & Systems (2nd Edition)
By A. V. Oppenheim, A. S. Willsky &S. H. Nawa
Signal & Systems
By Prentice Hall
Reference Book
Signal & Systems (2nd Edition)
By S. Haykin&B.V. Veen
Signals & Systems
By Smarajit Gosh

4. WHAT IS SIGNALS?
 A signal is a function of independent variable that
carries information.
 Physical quantity that varies with time, space or any
other independent variable.
 E.g. Electrical Signals Voltage varies with time
t
v

5. SIGNALS (EXAMPLES)
 Acoustic Signals Audio or speech signals
 ECG Signals

6. IMAGE

7. SIGNAL
 The image
7

8. SIGNAL
• It is the variation pattern that conveys the information, in a
signal
• Signal may exist in many forms like acoustic, image, video,
electrical, heat & light signal 8

9. SIGNALS
One –Dimensional Signal
Depends on single variable e.g. Speech signal
Multidimensional Signals
Depends on two or more variables e.g. image

10. WHAT IS SYSTEM?
 An entity that manipulates one or more signals to
accomplish a function, thereby yielding a new signal.
 E.g Speech recognition system
systeminput output
Identified

11. The camera
Signal & Systems
o Study of signals and their interaction with systems.
Image

12. MATHEMATICAL REPRESENTATION
 A signal can be represented as a function of one or more
independent variables
 Examples
    20sin  tttv
 ts
12
t

13. MATHEMATICAL REPRESENTATION
 The image is a function of two spatial (3D)variables
 yxs ,
13

14. TYPES OF SIGNALS
 Two types of signals
Continuous time signals
• Continuous time signals are defined for all instant of
time
• Independent variable enclosed in parenthesis (.)
• Denoted by x(t)
• Represented by function or graph
V(t)=sin(t) o≤t≤2
t
v

15. CONTINUOUS-TIME SIGNALS
 A value of signal exists at every instant of time
t
15
Independent variable
Independent variable
t

16. DISCRETE TIME SIGNAL
• Defined on discrete instant of time.
• Independent variable is enclosed in brackets [.]
• Denoted by x[n]
• Discrete signal is obtained by taking samples of analog
signal at discrete instant of time.
X[1]
n0 1 2 3 4-1-2-3-4
X[n]
X[2]
X[-1]

17. CONTINUOUS AND DISCRETE SIGNALS
 Examples of continuous signals
 Speech, video, image
 The variation of atmospheric pressure, wind speed
 Examples of discrete signal
 Demographic data, weekly stock position of a company
3/26/2019UAJK-MZD

18. REPRESENTATION
OF DISCRETE TIME
SIGNALS

19. REPRESENTATION OF DISCRETE TIME
SIGNALS
 Fours ways for representing discrete time signals.
Graphical representation of signal
Consider a signal x[n] having values
x[-2]=-4,x[-1]=1,X[0]=2, x[1]=1,x[2]=2
X[1]
n0 1 2-1-2
X[n] X[2]
X[-1]

20. FUNCTIONAL REPRESENTATION OF DISCRETE
SIGNALS
 Signals can be represented using functional
representation as:
x[n]= -4 for n= -2
1 for n=-1
2 for n=0
1 for n=1
2 for n=2
Tabular representation of discrete signals
• In this method, sampling instant n and the magnitude of
signal at the sampling instant are represented in tabular
form.
n -2 -1 0 1 2
X[n] -4 1 2 1 2

21. SEQUENCE REPRESENTATION OF DISCRETE
SIGNALS
 A finite duration sequence can be represented as:
x[n]= { 2, -4, 3, 0, 1, 3, 2 }
o The arrow denotes n=0 term.
o When no arrow is indicated then first term indicates the n=0 term.
x[n]= { 2, 4, 3, 1, 5 }