1. SIGNALS AND SYSTEMS
Lab 03
Lab Title: SIGNALS AND THEIR CLASIFICATIONS
Objective: In this lab, we will get an understanding of the following topics:
⮚ Continuous Time vs. Discrete Time Signals
⮚ Analog vs. Digital Signals
⮚ Periodic vs. Aperiodic Signals
⮚ Even vs. Odd Signals
⮚ Energy vs. Power Signals
Tool Used: Matlab.
Description:
What is a signal ?
A flow of information.
● (Mathematically represented as) a function of independent variables such as time (e.g.
speech signal), position (e.g. image), etc.
● A common convention is to refer to the independent variable as time, although may in
fact not.
Example signals
● Speech: 1-Dimension signal as a function of time s(t);.
● Grey-scale image: 2-Dimension signal as a function of space i(x,y)
Types of signals
The independent variable may be either continuous or discrete
Continuous-time signals
Discrete-time signals are defined at discrete times and represented as
sequences of numbers
The signal amplitude may be either continuous or discrete
Analog signals: amplitude is continuous
Digital signals: Amplitude is discrete
Computers and other digital devices are restricted to discrete time
Signal processing systems classification follows the same lines
Signal Processing
Modifying and analyzing information
Representation, transformation and manipulation of signals and information they contain

2. Applications of Signal Processing
Speech processing
Enhancement – noise filtering
Coding
Text-to-speech (synthesis)
Recognition
Image processing
Enhancement, coding, pattern recognition (e.g. OCR)
Multimedia processing
Media transmission, digital TV, video conferencing
Communications
Biomedical engineering
Navigation, radar, GPS
Control, robotics, machine vision
Continuous Time vs. Discrete Time Signals
Continuous Time Signals:
Continuous Time Signal is the one whose domain is uncountable, we don’t care about
range. For storing the continuous time signal you need infinite memory which is not
possible in any real system. So, finite no of samples of a continuous time signals are
stored. For plotting the continuous time signals we use plot command, which simply
connects the values of intermediate samples, gives us the illusion of continuous time
signals. In MATLAB we can plot any continuous time signal for example using plot
command as follows:
%Continuous Time Signal Example
Discrete Time Signals:
Discrete Time Signals are those signals which are purely based upon domain, whose domain is

3. Countable. We don’t care about range of the signal.
In MATLAB we can plot any discrete time signal for example Asin(wn+q) using stem
command as follow
%Discrete Time Signal Example
Analog vs. Digital Signal:
This classification of signal is purely based on range, we don’t care about the domain.
Analog Signals:
Analog Signals can take infinite values in range. In MATLAB we can plot any Analog signal
for example Asin(2πft+ ) using plot command as follows:
∅
% Analog Signal Example
A=2; %Amplitude
f=2; %Frequency
phase=pi; %Phase
t=(0:0.01:2*pi)/pi; %Time axis

4. plot(t,A*sin(2*pi*f*t+phase));
title('Example of Analog Signal');
xlabel ('Time (pi Units)');
ylabel ('Amplitude');
We can also plot analog signal using stem command.
%Example of Analog Signal

5. Digital Signal:
Digital signal is the one which can take countable finite values in range. In MATLAB we can
plot digital signal for example a random bipolar data using stem or plot Commands.
%Digital Signal Example

6. Square wave is another example of Digital signal.
%Digital Signal Example
Periodic vs. Aperiodic Signals:
Periodic Signals:
A signal which repeats its pattern after a specific interval of time is called periodic
signal. A signal which does not repeat its pattern after a specific interval of time is called
aperiodic signal.

7. Where N is the fundamental time period
In MATLAB we can generate a periodic signal using following code:
%Periodic Signal Example
b) Aperiodic Signals:
The opposite of a periodic signal is an aperiodic signal. An aperiodic function never repeats,
although technically an aperiodic function can be considered like a periodic function
with an infinite period.
In MATLAB we can generate an aperiodic signal using following code:
%Aperiodic Signal Example

8. Even vs. Odd Signals
a) Even Signals:
If x(-n) = x(n) then signal is called even signal. Cosine function is an example of even signal.
%Even Signal Example
b) Odd Signals:
If x(-n) = -x(n) then signal is called odd signal. Sine function is a n example of odd signal.
Energy vs. Power Signal:

9. a) Energy Signal:
A signal x(t) is said to be energy signal if and only if the total normalized energy is finite and
non-zero. Non-periodic signals are energy signals.
Total energy of a signal x(t) can be expressed as:
b) Power Signal:
The signal x(t) is said to be power signal, if and only if the normalized average power p is
finite and non-zero. Practical periodic signals are power signals.
Total power of a signal x(t) is given by:
Example: Following is example of Energy signal:
Using MATLAB Symbolic Maths, we can find its energy as following
syms t T
x=2;
E=limit((int(x^2,t,-1,1)),T,inf)
The energy answer will be: E = 8
For an energy signal, power will always be equal to zero
P=limit((1/(2*T))*(int(x^2,t,-1,1)),T,inf)
P = 0
Example: Following is the example of Power Signal
syms t T
x = t;
P = limit((1/(2))*(int(x^2,t,-1,1)),T, inf)
P = 4/3
For a power signal, energy is always equal to .
E = limit((int(x^2,t,-T,T)),T,inf)
E = Inf
Exercise:
Q#1 Even and Odd Signals
Give two examples of Odd and Even signals each and plot them in MATLAB.
Q#2 Find the energy and power of the following signal

10. Lab performed on (date): ___________ Signature: ______________
Checked by: ________________________ Date: ______________
Marks Awarded: ____________
Comments: