1. Signal Processing: Propaedeutics
Junwei Cao (曹军威) and Junwei Li (李俊伟)
Tsinghua University
Gravitational Wave Summer School Kunming, China, July 2009 1

2. Signals Signals: carriers in information transmitting
Deterministic signals
Random signals
Deterministic
Random

3. Time vs. Frequency

4. Unit Impulse
Dirac delta definition

5. Fourier Series Periodic signal f(t) period: Angular frequency:

6. Euler Formula
According to Euler formula
Rewrite Fourier series

7. Discrete vs. Continuous
When
periodic non-periodic
From discrete to continuous
Discrete
Continuous

8. Fourier Transformation
From Fourier series
Set

9. Fourier Inverse Transformation

10. An Example

11. An Exercise A periodic cosine signal Requirement:
Its Fourier transform
Draw the waveform of

12. Answers

13. Thank You !
Junwei Cao 13