Signal Processing: Propaedeutics

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Presentation transcript:

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

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

Time vs. Frequency

Unit Impulse Dirac delta definition

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

Euler Formula According to Euler formula Rewrite Fourier series

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

Fourier Transformation From Fourier series Set

Fourier Inverse Transformation

An Example

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

Answers

Thank You ! Junwei Cao jcao@tsinghua.edu.cn http://ligo.org.cn 13