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.