ECE 445S Real-Time Digital Signal Processing Laboratory - Lecture 5

Announcements: Remaining Relevant

Lecture

• Lecture 5 slides on Finite Impulse Response Filters in PowerPoint format.
  • "ABC", Jackson 5.
    Performed Feb. 21, 1970, on Bandstand, three days before song was released.
    #1 hit. Song inducted into Grammy Hall of Fame on Nov. 7, 2016.
    Jackson 5 inducted into the Rock and Roll Hall of Fame in 1997.
  • Fall 2024 Part 1
    • Board. Decomposing a discrete-time signal
    • Demos. continuous-time and discrete-time convolution in MATLAB
  • Fall 2024 Part 2
    • Handout. Designing averaging filters
    • Board. FIR Implementation Complexity
    • Board. FIR Filter in Integer Data and Arithmetic
    • Board. Ideal Delay Transfer Function
  • Fall 2024 Part 3
  • Fall 2024 Part 4
    • Demo #1: imageRampsCosines.m to introduce images and their frequencies
    • Demo #2: Cascading FIR filters image processing demo from DSP First

• Sound Shield acoustic noise masking senior design project video and filter bank

• Spring 2014 lecture on FIR filters on Video: Part 1, Part 2, Part 3 and Part 4.

Supplemental Information

• FIR filter introduction
• Handout Q Four ways to filter a signal
• "Wireless Surface Acoustic Wave Sensors", by Kerem Durdag, Sensors and Transducers Journal, July 2009. Surface acoustic wave filters are FIR filters.
• Spring 2024 marker board notes
  • Spring 2024 Part 1
    • Board. Using chirp signals for system identification
    • Board. Spectrogram review
    • Board. Decomposing a discrete-time signal
  • Spring 2024 Part 2
    • Board. Transfer function of an ideal delay in the z-domain
    • Board. ROC for z-transform of a^n u[n]
    • Board. Z-transform of the sum of two signals
    • Board. Connection between Z and discrete-time Fourier transforms
    • Board. Delay in time leads to a shift in phase
    • Board. Linear phase
    • Board. Connection between frequency domains
    • Board. Eigenfunctions
  • Spring 2024 Part 3
    • Board. Photo detector array
    • Board. Derivation of linear phase response for an averaging filter
    • Demo #1: imageRampsCosines.m to introduce images and their frequencies
    • Demo #2: Cascading FIR filters image processing demo from DSP First
    • Board. Wordlength expansion due to FIR filtering
  • Spring 2024 Part 4
    • Board. Review of Cascades of LTI Systems
    • Board. FIR Linear Phase due to Symmetry in Impulse Response
    • Demo #3: ImagePhaseDemo.m to show importance of phase information in images (slide 5-27)
      • Take FFT, set phase to zero, take inverse FFT
      • Take FFT, set magnitude to 1, take inverse FFT, display imaginary part
      • Take FFT, set magnitude to 1, take inverse FFT, display real part
      • Original Image
    • Handout: Designing Averaging Filters
  • Interactive demo for filtering audio signals
• Fall 2023 Notes
  • Fall 2023 Part 1
    • Board. LTI review plus convolution
    • Demos. continuous-time and discrete-time convolution in MATLAB
    • Board. Lowpass Filtering using convolution demo
    • Handout: Designing Averaging Filters
  • Fall 2023 Part 2
    • Board. Convolving with Rectangular Pulses and ideal delay transfer function
    • Board. Forward Z-transform and DTFT similarities
    • Board. LTI System Magnitude and Phase Response
  • Fall 2023 Part 3
    • Review of FIR Filters and Group Delay
    • Demo #1: imageRampsCosines.m to introduce images and their frequencies
    • Demo #2: Cascading FIR filters image processing demo from DSP First
      • 2-D Filtering
      • Wordlength expansion due to FIR filtering
    • Demo #3: ImagePhaseDemo.m to show importance of phase information in images (slide 5-27)
      • Take FFT, set phase to zero, take inverse FFT
      • Take FFT, set magnitude to 1, take inverse FFT, display imaginary part
      • Take FFT, set magnitude to 1, take inverse FFT, display real part
      • Original Image
  • Interactive demo for filtering audio signals
• Spring 2023 marker board notes
  • Spring 2023 Part 1
    • Equalization and FIR Filter Initial Conditions
    • Demos: continuous-time and discrete-time convolution in MATLAB
    • Handout: Designing Averaging Filters
    • Lecture Notes by TA Alice Liu
  • Spring 2023 Part 2
    • Z transforms
  • Spring 2023 Part 3
    • LTI system behavior in time, frequency and z domains
    • Frequencies captured during sampling
    • Demo #1: imageRampsCosines.m to introduce images and their frequencies
    • Demo #2: Cascading FIR filters image processing demo from DSP First
    • Lecture Notes by TA Dan Jacobellis
  • Spring 2023 Part 4
    • Demo: ImagePhaseDemo.m to show importance of phase information in images (slide 5-27)
      • Take FFT, set phase to zero, take inverse FFT
      • Take FFT, set magnitude to 1, take inverse FFT, display imaginary part
      • Take FFT, set magnitude to 1, take inverse FFT, display real part
      • Original Image
• Fall 2022 marker board notes
  • Part 1
    • Bounded-input bounded-output (BIBO) stability introduction and handout
    • Discrete-time convolution derivation step
  • Part 2
    • MATLAB demos of continuous-time and discrete-time convolution
    • Finite observation of a signal
    • LTI systems convolve in time and filter in frequency
    • DT signal with the highest frequency
    • Transfer function of an ideal delay
  • Part 3
    • Connection between z and Discrete-time Fourier transforms
    • Time delay causes phase shift, and definitions of group and phase delay
    • Image capture using photodetector array
    • imageRampsCosines.m to introduce images and their frequencies
  • Part 4
    • Cascading FIR filters image processing demo from DSP First
      • Averaging and first-order difference filters
      • Wordlength expansion due to FIR filtering
• Spring 2022 marker board notes
  • Part 1: Convolution and Z-transforms
    • Filtering out-of-band noise to improve SNR
    • LTI FIR filter difference equation and initial conditions
    • Derivation of discrete-time convolution
    • Transfer function for an LTI Ideal Delay
  • Part 2: Convolution Demos and Frequency Responses
    • MATLAB demos of continuous-time and discrete-time convolution
    • Notes on convolution demos
    • Discrete-Time Fourier Transforms
  • Part 3: Image Processing Demonstrations
    • Review: LTI systems in time and frequency domains
    • Delay in time becomes shift in phase
    • imageRampsCosines.m to introduce images and their frequencies
    • First-order difference filter frequency response and phase response discontinuity
    • FIR filters in cascade (lecture slides 5-21 to 5-25)
  • Part 4: More Image Processing Demonstrations
    • Number of bits needed for LTI in the FIR filters in cascade demo
    • ImagePhaseDemo.m to show importance of phase information in images (slide 5-27)
      • Take FFT, set phase to zero, take inverse FFT
      • Take FFT, set magnitude to 1, take inverse FFT, display imaginary part
      • Take FFT, set magnitude to 1, take inverse FFT, display real part
      • Original Image
• Fall 2021 marker board notes
  • Part 1: equalization, FIR run-time complexity, and LTI system time responses
  • Part 2: z-transform to DTFT and linear phase and constant group delay
• Spring 2021 notes from the marker board
  • Part 1: discrete-time frequency domain periodicity and equalization
  • Part 2: takeaways, convolution derivation, convolution demos and z-transforms
  • Part 3: takeaways, frequency domains, group delay, and bandpass transmission
  • Part 4: Spring 2014 FIR filtering of images video 11:10 to 33:47 and slides 5-19 to 5-21, and importance of linear phase
• Fall 2020 notes from the marker board
  • Linear vs. circular buffers
  • Equalization (slide 5-3) and convolution (slide 5-8)
  • Time shift leads to phase shift (slides 5-12 and 5-13)
  • LTI systems do not create new frequencies (slide 5-14)
  • Takeaways, image ramps & cosines, and averaging & first-order difference filters (slides 5-18 to 5-20)
  • Group delay for averaging & first-order difference filters (slide 5-20)
• "Transients in FIR Filtering of Tonebursts", Gerald Cain, April 4, 2016. Linear phase FIR filtering of a sinuosidal tone to show effects of group delay.

Last updated 10/02/24. Send comments to bevans@ece.utexas.edu