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

Lecture by Prof. Brian L. Evans

Announcements: Student Well-Being and Course Info

Lecture

Lecture slides on Introduction in PowerPoint format.
- Your goals for learning and growth (Spring 2025)
  - Be good at ECE 313 Linear Systems and Signals again
  - Learn more about image processing techniques
  - Expand horizons from the embedded work
  - Work on passive and active digital filters
  - Work more on software receiver design
  - Audio processing
  - Skills for senior design project
- 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
  - Audio equalization (lecture slide 0-9)
- 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

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 01/15/25. Send comments to (Mailbox) bevans@ece.utexas.edu