Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

   

Courses

EE 20. Structure and Interpretation of Systems and Signals

Current Schedule (Spring 2014)

Description

Course objectives: This course introduces mathematical modeling techniques used in the study of signals and systems. Its intention is to promote rigorous thinking and mathematical intuition about, and an appreciation for a multidisciplinary study of, signals systems through precise modeling.

Topics covered:

  • Mathematical Foundations - Sets and functions; Fundamentals of mathematical logic; Complex algebra (including complex-valued functions); Basic linear algebra (matrix-vector manipulations, eigenanalysis of 2x2 matrices; Vector-space concepts (e.g., axioms describing vector spaces, basis, dimension, inner products, orthogonal basis expansions).
  • Signals - Signals as functions: continuous time, discrete time; Signals as vectors in an appropriately-defined vector space having an appropriately-defined inner product; Orthogonality of signals; Two-dimensional space continuum; Discrete-space: discrete time and continuous space, discrete time and mixed space, discrete time and space, discrete events, discrete events and discrete time; Sequences.
  • Sinusoids - Periodic signals, sinusoids-phase and amplitude, complex numbers, complex signals, complex exponentials; Phasors, amplitude modulation, frequency modulation.
  • Spectrum - Summing sinusoids, approximating periodic signals, harmonics and musical sounds, beat notes, two-dimensional sinusoids; Approximating images.
  • Sampling - Analog-to-digital conversion, aliasing, downsampling, digital-to-analog conversion, upsampling, oversample CD players.
  • Systems - Filters, Running average filter, Two-dimensional running average filter, FIR filters; Linearity; Time invariance; Causality; Memory; Impulse response; Convolution.
  • Frequency Response and Filtering - Sinusoidal input, complex sinusoidal input, transfer function; Filtering audio signals, blurring and sharpening images.
  • Fourier Series and Transforms - Fourier series using vector-space concepts; Signals viewed as vectors; Harmonically-related sinusoids and complex exponentials are viewed as orthogonal vectors in an appropriately-defined vector space; Discrete Fourier series (DFS/DFT); Continuous-time Fourier series (FS); Discrete-time Fourier transform (DTFT); Continuous-time Fourier transform (CTFT).
  • Z Transform - Unit delay; Polynomials to represent signals; Z transform as an operator; Convolution; Poles and zeroes and their relationship to frequency response (e.g., digital lowpass, bandpass, notch, and comb filters).
  • Spectrum Analysis - Spectra of periodic and aperiodic signals; Time and frequency sampling; Amplitude modulation; Spectrograms.
  • Nonlinear Systems - First- and second-order continuous-time and discrete-time autonomous systems: equilibrium point identification, stability analysis of equilibrium points, sketching vector fields, sketching phase portraits; Frequency modulation; synthesis of musical sounds; hard limiting; Edge detection; Feedback; Fractals and chaos; Noise in musical sounds and images.
  • State Machines - Events, I/O traces; State and finite state; Moore machines; Deadlock freedom; Trace language of a state machine; Hiding of events
  • Relating State - Concrete and abstract system descriptions; Nondeterminism; Safety requirements: The simulation relation; Simulation implies trace inclusion, layers of abstraction.
  • Composing State - Parallel components, I/O synchronization, interleaving of internal events; Product state space, intersection of trace languages; Composition preserves simulation, control, state equivalence; State minimization, machine equivalence, bisimilarity implies simulation; Composition preserves bisimilarity.
  • Discrete Events - Time stamps, non-uniform sampling, pulse position modulation; Zeno signals, communicating automata, communication networks; Speech and video on communication networks.

General Catalog

Undergraduate Student Learning Goals