1. Continuous-Time Fourier Transform
主講者：虞台文

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

3. Continuous-Time Fourier Transform
Introduction

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

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

6. Two Forms for Fourier Series
Sinusoidal
Form
Complex
Form:

7. How to Deal with Aperiodic Signal?
f(t)
If T, what happens?

8. Continuous-Time Fourier Transform
Fourier Integral

9. Fourier Integral
Let

10. Fourier Integral
F(j)
Synthesis
Analysis

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

12. Continuous-Time Fourier Transform

13. Fourier Transform Pair
Inverse Fourier Transform:
Synthesis
Fourier Transform:
Analysis

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

15. Continuous Spectra
FR(j)
FI(j)
|F(j)|
()
Magnitude
Phase

16. Example 1 -1 t
f(t)

17. Example 1 -1 t
f(t)

18. Example t
f(t)
et

19. Example t
f(t)
et