Course Outline

Overview

The previous course, EE102A, introduced Fourier based methods for analyzing signals. These are powerful tools that have broad application in communications, imaging, and signal processing in general. However, there are important problems which Fourier methods fail, such as analyzing systems that can grow (populations, bank accounts) or systems that are potentially unstable (aircraft, robot arm, amplifiers). These can be solved with the Laplace transform (LT) in continuous time, or the Z-transform (ZT) in discrete time. In this course we will study the LT and ZT, and the additional powerful signal analysis tools they enable.

Exams

The exams will be open book and open notes.

Outline

Section 1: Review of Fourier Representations

  • Fourier transform (FT)

  • Discrete time Fourier Transform (DTFT)

  • Discrete time Fourier Series (DTFS)

  • When to use these

  • When do you need something more powerful

Section 2: Signal Sampling and Reconstruction

  • Review of the sampling theorem

  • Bandpass Sampling

  • Decimation and Interpolation

Section 3: FIR Filters

  • Finite impulse response filters (FIR) verses infinite impulse response filters (IIR)

  • Ideal filters, and types of filters

  • Design of FIR filters

  • Window functions

Section 4: Discrete Fourier Transform (DFT)

  • Relation to Fourier Series

  • Circular convolution

  • Linear convolution with the DFT

  • Matrix representation

Section 5: Laplace Transform (LT)

  • Relation to the Fourier transform

  • Linear time invariant (LTI) systems

  • Computing and interverting the LT

  • Frequency response and Bode plots

  • Solving differential equations

  • Stability of LTI systems

Section 6: Feedback Systems

  • Applications of feedback

  • Feedback control

  • Stability of feedback systems

  • Linearization of non-linear systems

Section 7: Z Transform (ZT)

  • Relation to the DTFT

  • Discrete time LTI systems

  • Computing and inverting the ZT

  • Solving difference equations

  • Stability of DT LTI systems

Section 8: Infinite Impulse Response Filters (IIR)

  • Impulse invariant design

  • Bilinear transformation