Fourier Transforms

LIST OF PAGE CONTENT

• Introduction
• Limitation Of FS
• Need Of FT
• Derivation of the FT of a Non-periodic Signal from the FS of a Periodic Signal
• Magnitude and Phase Representation of FT
• Existence of FT
• FT of Standard Signals
  • Impulse Function
  • Single-sided Real Exponential Function
  • Double-sided Real Exponential Function
  • Complex Exponential Function
  • Constant Amplitude
  • Signum Function
  • Unit Step Function
  • Rectangular Pulse
  • Triangular Pulse
  • Cosine Wave
  • Sine Wave
• Properties of Continuous Time FT
  • Linearity Property
  • Time Shifting Property
  • Frequency Shifting Property (Multiplication by an Exponential)
  • Time Reversal Property
  • Time Scaling Property
  • Differentiation in Time Domain Property
  • Differentiation in Frequency Domain Property
  • Time Integration Property
  • Convolution Property or Theorem
  • Multiplication Property or Theorem
  • Duality (Symmetry) Property
  • Modulation Property
  • Conjugation Property
  • Autocorrelation Property
  • Parseval’s Relation or Theorem or Property
  • Area under the Curve
  • Fourier Transform of Complex and Real Functions
• FT of a Periodic Signal

Introduction

Limitation Of FS

Need Of FT

Derivation of the Fourier Transform of a Non-periodic Signal from the Fourier Series of a Periodic Signal

Magnitude and Phase Representation of FT

Existence of FT

Dirichlet's Conditions

FT of Standard Signals

Impulse Function

Single-sided Real Exponential Function

Double-sided Real Exponential Function

Complex Exponential Function

Constant Amplitude

Signum Function

Unit Step Function

Rectangular Pulse

Triangular Pulse

Cosine Wave

Sine Wave

Properties of Continuous Time FT

Linearity Property

Time Shifting Property

Frequency Shifting Property (Multiplication by an Exponential)

Time Reversal Property

Time Scaling Property

Differentiation in Time Domain Property

Differentiation in Frequency Domain Property

Time Integration Property

Convolution Property or Theorem

Multiplication Property or Theorem

Duality (Symmetry) Property

Modulation Property

Conjugation Property

Autocorrelation Property

Parseval’s Relation or Theorem or Property

Area under the Curve

Fourier Transform of Complex and Real Functions

FT of a Periodic Signal