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Signal Processing: Propaedeutics

Signal Processing: Propaedeutics. Junwei Cao ( 曹军威 ) and Junwei Li ( 李俊伟 ) Tsinghua University Gravitational Wave Summer School Kunming, China, July 2009. Signals. Signals: carriers in information transmitting Deterministic signals Random signals. Deterministic. Random.

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Signal Processing: Propaedeutics

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  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

  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: • 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 jcao@tsinghua.edu.cn http://ligo.org.cn

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