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ES 400 Review

ES 400 Review. Continuous Time Signal. Goal: Use mathematics to analyze circuits and system. . Typical Process. Use math to describe signal Property of a system Frequency Analysis Techniques Fourier series (periodic signal) Fourier Transform (periodic/aperiodic signal)

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ES 400 Review

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  1. ES 400 Review

  2. Continuous Time Signal • Goal: Use mathematics to analyze circuits and system.

  3. Typical Process • Use math to describe signal • Property of a system • Frequency Analysis Techniques • Fourier series (periodic signal) • Fourier Transform (periodic/aperiodic signal) • Laplace Transform (Even more general than Fourier Transform) • Applications of Mathematical Analysis Techniques

  4. Describe Signal Mathematically • Time reversal • Time scaling • Time shifting • Amplitude transformation • Even/Odd function • Step function • Impulse function

  5. Properties of a System • Causality • Stability • Time Invariance • Linearity • … • Convolution

  6. Fourier Series

  7. Fourier Series Vs. Fourier Transform • We use Fourier Series to represent periodic signals • We will use Fourier Transform to represent non-period signal.

  8. Applications of Fourier Transform • Sampling • Bandwidth • Energy Density • Power Spectral Density • Bode Plot • Reconstruction of Signals from Sampled Data

  9. Applications of Fourier Transform in Communication • Sinusoidal amplitude modulation • Pulse Amplitude Modulation

  10. Highlights of Laplace Transform • Region of Convergene (ROC) • Differentiation Property • Integration Property • Application to C and L • Unit Step Function • Exponential Decay • Initial Value Theorem • Final value Theorem

  11. Application of Laplace Transform • Natural Response of an RL Circuit • Natural Response of an RC Circuit • Oscillator Analysis

  12. Time and Date for the Final • 12/10 (Monday) • 2:00 pm. to 3:50 pm. • Place: Salazar 2006

  13. Final Exam • 2 pages of 11.5” x 8.5” (front and back) • Topic Outline • Laplace Transform (Emphasis!) • Properties • Application of Laplace Transform • Applications of Fourier Transform • Fourier Series • And everything else

  14. What is next? • If you are a junior: • You should enroll in Microprocessor, if you have had ES314 and Digital Logic Design (ES 220) • You should enroll in Analog & Digital Communication, if you have had ES314.

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