ECE 445S Real-Time Digital Signal Processing Laboratory - Lecture 0

Announcements: Student Well-Being and Course Info

Lecture

• Lecture slides on Introduction in PowerPoint format.
  • Your goals for learning and growth?
    • Biomedical - brain signals
    • Wireless communications - RF
    • Global navigation satellite systems - differential GNSS
    • Image/video processing -- general and for robotics
    • Audio and video processing
    • Signal integrity
  • Signal quality vs. run-time implementation complexity
  • Signal quality measures
    • Signal-to-noise ratio (SNR)
    • Frequency weighted SNR (WSNR)
    • Communication systems -- bit rate, bit error rate, received signal strength
  • Signal-to-noise ratio (SNR)
    • Application-independent signal quality measure (larger value is better)
    • SNR = Signal Power / Noise Power
    • SNR is unitless
    • SNR_dB = 10 log₁₀ SNR
    • SNR does not appear in any pre-requisite courses except possibly ECE 319K Intro to Embedded Systems
  • Frequency weighted SNR (WSNR)
    • use a filter to represent frequency distortion in observing the signal, e.g. lowpass filter for the LTI model of the human auditory and visual systems
    • filter the signal and compute the power of the filtered signal
    • filter the noise and compute the power of the filtered noise
    • divide the two
  • Run-time implementation complexity measures
    • Economic cost for the materials
    • Power consumption
    • Delay
    • Storage (memory)
    • Memory input/output rates
    • Computational complexity
    • Run time
    • Robustness (error resilence)
  • Courses using Python include M 340L Matrices & Matrix Comp., ECE 351M Digital Signal Processing, ECE 460J Data Science Lab, ECE 461L Software Eng. Lab, and ECE 461P Data Science Principles.
  • Comparison of ECE 445S with ECE 351M and other related courses
  • Common Signals in Matlab handout (slides)

• Continuous-time Fourier transforms
  • "But what is the Fourier Transform? A visual introduction", by 3Blue1Brown, Jan. 26, 2018
  • Introduction to Fourier transforms notes from an office hours discussion
  • Videos: Brian Douglas (13:03) - Darryl Morrell, Part 1 (9:02) - Darryl Morrell, Part 2 (11:07)
  • Signals & Systems slides: Frequency Response - Fourier Transforms - Sampling & Reconstruction
  • Fourier transform properties:
    • Sections 2.1-2.7 of Software Receiver Design
    • Section 7.3 in Lathi's Linear Systems and Signals (second edition)
    • Section 5.5 in Roberts' Signals and Systems
    • Sections 11-4 to 11-8 in McClellan, Schafer and Yoder's Signal Processing First

• Spring 2014 lecture on video: Part 1 and Part 2

Supplemental Material

• Spring 2025
  • Adaptive systems
    • Discussed throughout the second half of the course
    • Consider a system with a tunable parameter that is producing output x vector
    • We would like the system to produce output y vector
    • We can adapt the tunable parameter so that the system output x vector moves closer in Euclidean distance to y vector
    • Board: Audio equalization (lecture slide 0-9)
• Fall 2024
  • Signal quality and implementation complexity measures
  • Algorithm analysis
    • The fast Fourier transform (FFT) is a fast algorithm for computing the discrete Fourier transform (DFT)
    • The DFT transforms a sampled time-domain signal (vector) and produces a sampled frequency-domain signal (vector)
    • Given N is the number of samples, the DFT takes N^2 complex-valued multiplications
    • Wnen N is a power of two, the FFT takes 0.5 N log₂ N complex-valued multiplications
• Spring 2024
  • Course theme: algorithm design tradeoffs in signal quality vs. run-time implementation complexity
• Fall 2023 Algorithm design tradeoffs in signal quality vs. run-time implementation complexity
  • Examples
  • Communication systems
• Spring 2023 Marker board notes on signal quality and run-time complexity tradeoff examples
• IEEE Signal Processing Society

Last updated 08/27/25. Send comments to bevans@ece.utexas.edu