This document provides an introduction to signals and systems. It defines key concepts such as: - Signals contain information about some phenomenon and can be represented as functions of variables like time or frequency. - Systems respond to input signals by producing output signals. Examples of systems include electrical circuits, cameras, robots, and computer programs. - Signals can be continuous-time functions of a real-valued variable like time, or discrete-time functions of an integer variable. - Periodic, even, odd, exponential, and sinusoidal signals are introduced. - Major application areas of signals and systems concepts include communications, audio/speech processing, and circuit design.

1. SIGNALS & SYSTEMS
Name- Suchanda Banerjee
Roll No.- 10800120085
Batch- B
Branch- Computer Science & Engineering
Semester- 6
Asansol Engineering College

2. INTRODUCTION
 The concepts of signals and systems arise in a wide variety of areas, such as
communications, circuit design, biomedical engineering, power systems, speech
processing, etc.
 The ideas and techniques associated with these concepts play an important role in such
diverse areas.
 Although the physical nature of the signals and systems that arise in these various
disciplines may be drastically different, two basic features in common are:
 The signals, which are functions of one or more independent variables, contain information
about the behavior or nature of some phenomenon.
 The systems respond to particular signals by producing other signals or some desired behavior.
 Examples of signals and systems.
 Voltages and currents as functions of time in an electrical circuit are examples of signals. A
circuit is itself an example of a system, which responds to applied voltages and currents.
 A camera is a system that receives light from different sources and produces a photograph.

3.  Automobile driver depresses the accelerator pedal.
The automobile responses by increasing the speed of the vehicle.
System is the automobile, pressure on pedal is the input signal, the automobile speed is the
response or output signal.
 Digitized electrocardiogram as input to a computer program for an automated diagnosis
of electrocardiogram.
The program responses by estimating parameter ( the heart rate of the patient).
System is the computer program, digitized electrocardiogram is the input signal, the heart rate is
the response or output signal.
 Control input signal to a robot arm.
The robot responses by producing movement of the arm.
System is the robot arm, control electrical signal is the input signal, the movement of the arm is
the response or output signal.

4. MAJOR APPLICATION AREAS
 Communications
 Audio and Speech Processing
 Image, Video Processing
 Acoustics
 Circuit Design
 Seismology
 Biomedical Engineering
 Bioinformatics
 Energy Generation and Distribution System
 Chemical Process Control
 Areonautics

5. OBJECTIVES AND APPLICATIONS
 When presented with a specific system- We are interested in characterizing it
in detail to understand how it will response to input signals.
Example:- Understanding of human auditory system, Vocal Tract System,
Economic system, Analysis of circuits, Determination of aircraft response
characteristic due to pilot commands & wind gusts.
 Designing of systems to process signals in particular ways.
Example:- Economic forecasting, Stock Market predicting, Restoration of
degraded or corrupted signals. For example, Speech communication with
background noise as in aircraft cockpit or car. Aim to retain the pilot voice
and get rid of the engine noise, Restoration/enhancement of old
recording/image.
 Image from deep space probes or earth-observing satellites represent
degraded versions of the scenes being imaged.
Why.. Because of equipment limitations, atmospheric effect, errors in signal
transmission in returning the image to earth.
Process by system to restore/enhance the images.

6.  Designing systems to extract specific pieces of information from signals.
Example include the estimation of heart rate from an electrocardiogram,
weather forecast.
 Designing of signals with particular properties.
For example, the design of communication signals must take into account
the need for reliable reception in the presence of distortion (due to
transmission media) and interference (such as noice).

7. SIGNALS
 Signals may describe a wide variety of physical phenomenon. It can be
represented mathematically as functions of one or more independent
variables:
For example:-
 Time: x(t)
 Frequency: X(f)
 Temperature
 Pressure
 And many other

8. DISCRETE-TIME & CONTINUOUS –TIME SIGNALS
 The course will cover concepts and techniques associated both with
continuous-time and discrete-time signals (and systems).
 Continuous-time signals are defined for a continuum of values of the
independent variables (the independent variable is continuous).
 Will always be treated as a function of t
 Parentheses are used to denote a continuous-time functions. For example, x(t).
 The independent variable t is a real-valued and continuous.
 Discrete-time signals are only defined at discrete items (the independent
variable takes on only a discrete set of values).
 Will always be treated as a function of n.
 Square brackets are used to denote discrete-time functions, for example, x[n].
 The independent variable n is an integer
 Examples:
 The speech signal as a function of time and atmospheric pressure as a function of
altitude are examples of continuous-time signals.
 The daily closing stock market index is an example of discrete-time signal.

9.  It is often useful to represent the signals graphically:

10. TYPES OF SIGNALS
We will be considering two basics types of signals:
 Continuous-time signals x(t)
We enclose the independent variable in parentheses ( . )
 Discrete-time signals x[n]
We use brackets [ . ] to enclose the independent variable.

11.  Continuous-time signals (and systems) have very strong roots in problems
associated with physics and more recently with electrical circuits and
communications.
 The techniques of discrete-time signals (and systems) have strong roots in
numerical analysis, statistics and time series analysis (associated with such
applications as the analysis of economic and demographic data).
 In the past decades, there has been a growing interrelationship between
continuous-time signals and systems and discrete-time signals and systems.
This has come from the dramatic advances in technology for the
implementation of systems and for the generations of signals. For example, it
is increasingly advantageous to consider processing continuous-time signals by
representing them with samples.
 This course develops the concepts of continuous-time and discrete-time
signals and systems in parallel. Since many of the concepts are similar, by
treating them in parallel, insight and intuition can be shared and both the
similarities and differences between them become better focused.

12. PEROIDIC SIGNALS
 Continuous-time -> x(t)=x(t+T)
It’s unchanged by a time shift to T.
 Discrete-time -> x[n]=x[n+N]
It’s unchanged by a time shift of N.

13. EVEN AND ODD SIGNALS
 Even signals:
x(-t)=x(t), for continuous-time signals
x[-n]=x[n], for discrete-time signals
 Odd signals:
x(-t)=-x(t), for continuous-time signals
x[-n]=-x[n], for discrete-time signals

14. EXPONENTIAL AND SINUSODIAL SIGNALS
 Continuous-time signal

15. PERIODIC COMPLEX EXPONENTIAL AND SINUSODIAL SIGNALS
Consider
For a periodic signal with period T,
Then
Or since,
We must have,
The period,