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)– Laplace Transform (Even more general than

Fourier Transform)

• Applications of Mathematical Analysis Techniques

Describe Signal Mathematically

• Time reversal• Time scaling• Time shifting• Amplitude

transformation• Even/Odd function• Step function• Impulse function

Properties of a System

• Causality• Stability• Time Invariance• Linearity• …• Convolution

Fourier Series

Fourier Series Vs. Fourier Transform

• We use Fourier Series to represent periodic signals

• We will use Fourier Transform to represent non-period signal.

Applications of Fourier Transform

• Sampling• Bandwidth• Energy Density• Power Spectral Density• Bode Plot• Reconstruction of Signals from

Sampled Data

Applications of Fourier Transform in Communication

• Sinusoidal amplitude modulation• Pulse Amplitude Modulation

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

Application of Laplace Transform

• Natural Response of an RL Circuit• Natural Response of an RC Circuit• Oscillator Analysis

Time and Date for the Final

• 12/10 (Monday)• 2:00 pm. to 3:50 pm.• Place: Salazar 2006

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

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.