This document provides an introduction and overview of continuous and discrete signals. It begins with introducing the author, Muhammad Salman, and his background and contact information. It then discusses the basics of continuous and discrete signals, including examples of generating unit impulse signals, sinusoidal signals, exponential signals, and complex exponential signals. The document concludes with generating an amplitude modulated signal and swept-frequency sinusoidal signal.

1. WIRELESS COMMUNICATIONS AND
NETWORKING
Lab 02: By Muhammad Salman
Continuous and discrete signals
Signal types
Various plotting operations

2. MY INTRODUCTION
• Name: Muhammad Salman
• Ph.D. Student at Intelligent Mobile Computing Lab (Inha University-South Korea)
• MS(Electronic Engineering) from Politechnico di Torino (Italy) and Chalmers
University of Technology (Sweden)
• Office location: 1008 (Hi-tech Building)
• Contact: salman@inha.edu (or) salman@nsl.inha.ac.kr (preferred)
• Alternative: +82-10-2134-4007 (Kakao/WhatsApp)

3. CONTINUOUS AND DISCRETE SIGNALS
Basics
• First of all:
• What is frequency, time period and signals?
• Periodic signal and aperiodic signals
• Deterministic signal or Stochastic signals
• What is analog and digital?
 Generation of Unit Discrete Time Unit impulse Signal:
• Unit Step: 𝑢 𝑛 =
1, 𝑛 ≥ 0
0, 𝑛 < 0
𝛿 𝑛 = 𝑢 𝑛 − 𝑢[𝑛 − 1]
-10 -5 0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Time index n
Amplitude
Unit Sample Sequence

4. CONTINUOUS AND DISCRETE SIGNALS
• Generation of Discrete Time Sinusoidal Signal:
• 𝑥 𝑛 = 𝐴𝑠𝑖𝑛 2𝜋𝑓𝑛 + 𝜑 = 𝐴𝑠𝑖𝑛(𝜔𝑛 + 𝜑)
0 5 10 15 20 25 30 35 40
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Sinusoidal Sequence
Time index n
Amplitude

5. CONTINUOUS AND DISCRETE SIGNALS
• Generation of Discrete Time Real exponential Signal:
• 𝑥 𝑛 = 𝐶𝛼𝑛
0 5 10 15 20 25 30 35
0
20
40
60
80
100
120
Time index n
Amplitude

6. CONTINUOUS AND DISCRETE SIGNALS
• Generation of Discrete Time Complex exponential signal:
• The complex exponential signal (or complex sinusoid) is defined as:
𝑥 𝑡 = 𝐴𝑒𝑗(𝜔0𝑡+∅)
(𝐴)
• Eq. A can also be expressed in Cartesian Form using Euler Formula:
𝑥 𝑡 = 𝐴𝑐𝑜𝑠 𝜔0𝑡 + ∅ + 𝑗𝐴𝑠𝑖𝑛(𝜔0𝑡 + ∅)
0 5 10 15 20 25 30 35 40
-2
-1
0
1
2
Time index n
Amplitude
Real part
0 5 10 15 20 25 30 35 40
-1
0
1
2
Time index n
Amplitude
Imaginary part

7. CONTINUOUS AND DISCRETE SIGNALS
• Amplitude Modulation Signal: More complex signals can be generated by performing the basic opertations on
simple signals. For example, an amplitude modulated signal can be generated by modulating a high-frequency
sinusoidal signal 𝑥𝐻 𝑛 = cos(𝜔𝐻𝑛) with low-frequency modulating signal 𝑥𝐿 𝑛 = cos(𝜔𝐿𝑛). The resulting Signal
𝑦[𝑛] is of the form:
• 𝑦 𝑛 = 𝐴 1 + 𝑚. 𝑥𝐿 𝑛 . 𝑥𝐻 𝑛
• 𝑦 𝑛 = 𝐴 1 + 𝑚. cos 𝜔𝐿𝑛 . cos 𝜔𝐻𝑛
Where m is modulating Index, is a number chosen to ensure that 1 + 𝑚. 𝑥𝐿 𝑛
is a positive for all n.
0 10 20 30 40 50 60 70 80 90 100
-1.5
-1
-0.5
0
0.5
1
1.5
Time index n
Amplitude

8. CONTINUOUS AND DISCRETE SIGNALS
• As the Frequency of a Sinusoidal signal is derivative of its phase with respect to time. To generate a swept-
frequency sinusoidal signal whose frequency increases linearly with time, The argument of Sinusoidal signal must
be a quadratic function of time. Assume that the argument is of the form 𝑎𝑛2
+ 𝑏𝑛 (i.e. the angular frequency is
2an+b). Solve for the value of a and b from the given conditions (minimum angular frequency and maximum
angular frequency)
0 10 20 30 40 50 60 70 80 90 100
-1.5
-1
-0.5
0
0.5
1
1.5
Swept-Frequency Sinusoidal Signal
Time index n
Amplitude

9. Questions ?