Lecture Notes: Signals and Systems - Types of Signals

Introduction

• Presenter: Professor (Author of 25+ Engineering books)
• Subject: Signals and Systems
• Focus: Types of signals (important for the entire subject)

Definition of a Signal

• A physical quantity that varies with one or more variables
• Examples in daily life: Traffic light signal, satellite signal, TV signal, mobile signal
• Practical examples: Sine wave signal, triangular wave signal, square wave signal

Types of Signals

1. Continuous or Discrete Signal

   • Continuous Signal (CT): Also known as continuous time signal, represented as X(t), changes continuously over time.
     • Mathematical representation: A sine wave - X(t) = A sin(ωt)
     • A = Amplitude, ω = Angular frequency (2πf)
   • Discrete Signal (DT): Consists of pulses, represented at certain instances of time, represented as X[n]
     • Mathematical representation: X[n] = A sin(ωn)

2. Periodic or Non-Periodic Signal

   • Periodic Signal: Repeats after a certain time period
     • Example: Sine wave, fundamental period denoted as T
     • Mathematical representation: X(t) = X(t + T)
   • Non-Periodic Signal: Does not repeat over time

3. Even or Odd Signal

   • Even Signal (Symmetric): Symmetric about the vertical axis
     • Condition: X(t) = X(-t)
   • Odd Signal (Anti-Symmetric): Anti-symmetric about the vertical axis
     • Condition: X(t) = -X(-t)

4. Energy or Power Signal

   • Energy Signal: Average normalized energy is non-zero and finite
     • Energy (E) is measured in joules
   • Power Signal: Average normalized power is non-zero and finite
     • Power (P) is measured in watts

5. Deterministic or Random Signal

   • Deterministic Signal: Can be expressed by a mathematical equation or truth table
     • Examples: Sine wave, cosine wave, triangular wave
   • Random Signal: Cannot be represented mathematically or by a truth table
     • Example: Noise

Summary

• Understanding the types of signals is crucial for the study of signals and systems.
• Application of these signal types is foundational for the entire subject.