ContinuousTime Fourier Transform Content l Introduction l Fourier

Continuous-Time Fourier Transform 主講者：虞台文

Content l Introduction l Fourier Integral l Fourier Transform l Properties of Fourier Transform l Convolution l Parseval’s Theorem

Continuous-Time Fourier Transform Introduction

The Topic Aperiodic Periodic Continuous Time Discrete Time Fourier Series Discrete Fourier Transform Continuous Fourier Transform

Review of Fourier Series l l Deal with continuous-time periodic signals. Discrete frequency spectra. A Periodic Signal f(t) t T 2 T 3 T

Two Forms for Fourier Series Sinusoidal Form Complex Form:

How to Deal with Aperiodic Signal? A Periodic Signal f(t) t T If T , what happens?

Continuous-Time Fourier Transform Fourier Integral

Fourier Integral Let

Fourier Integral F(j ) Synthesis Analysis

Fourier Series vs. Fourier Integral Fourier Series: Period Function Discrete Spectra Fourier Integral: Non-Period Function Continuous Spectra

Continuous-Time Fourier Transform

Fourier Transform Pair Inverse Fourier Transform: Synthesis Fourier Transform: Analysis

Existence of the Fourier Transform Sufficient Condition: f(t) is absolutely integrable, i. e. ,

Continuous Spectra FI(j ) | ) j |F ( ( ) FR(j ) Magnitude Phase

Example 1 -1 f(t) 1 t

Example 1 -1 f(t) 1 t

Example f(t) e t t

Example f(t) e t t