- Lecture 3 slides on
*Discrete-Time Signals and Systems*in PowerPoint format.- Spring 2024 Part 1
**Board:**Rectangular Pulse

- Spring 2024 Part 2
**Handouts:**Time-invariance for an integrator and delay under observation**Board:**Discrete-time unit step in Matlab**Board:**Linearity of an integrator when observing for t ≥ 0**Board:**Time invariance of a delay when observing for t ≥ 0**Board:**Amplitude modulation is time-varying (after lecture)**Board:**All pointwise operations are time-invariant (after lecture)

- Spring 2024 Part 3
**Board:**Effects of finite observation in time**Board:**Continuous-time frequencies captured by sampling**Board:**Sampling to obtain, and reconstruction of, a discrete-time impulse**Demo:**"Sandstorm", Darude, 1999, requested by Fall 2016 student. Synthesia Animation to show a time-frequency representation of the song.**Tuneup:**In-Lecture Assignment #1 on time-frequency representations**Board:**Frequency resolution in spectrograms

**Demo:**filtering audio signals. Noise and sweep signals filtered by lowpass, bandpass and highpass filters.

- Spring 2024 Part 1
- Spring 2014 lecture on video: Part 1 and Part 2

- Fall 2023 notes
- Fall 2023 Part 1
**Board:**Review of modulation and demodulation**Demo:**filtering audio signals. Noise and sweep signals filtered by lowpass, bandpass and highpass filters.

- Fall 2023 Part 2
**Demo:**"Sandstorm", Darude, 1999, requested by Fall 2016 student. Synthesia Animation to show a time-frequency representation of the song.**Board:**Review of System Properties and Linearity of integration under observation**Board:**Scalar gain has linearity property**Handouts:**Time-invariance for an integrator and delay under observation**Tuneup:**In-Lecture Assignment #1

- Fall 2023 Part 3
**Board:**. Review of chirps and spectrograms from in-lecture assignment #1**Board:**. Spectrogram windowing, and time and frequency resolution for a deeper dive into in-lecture assignment #1**Board:**Reconstruction of Discrete-Time Impulse**Board:**Sampling 30 kHz sinusoidal at 48 kHz**Demo:**Human hearing vs. age: How Old Are Your Ears? and large-scale study (Fig. 4)

- Designing averaging filters

- Fall 2023 Part 1
- Spring 2023 notes
- Part 1
- Dirac delta
- Filtering demo: lowpass filter and chirp signal (sweep)
- GPS
**Lecture Notes**by TA Dan Jacobellis

- Part 2
- System properties
**Lecture Notes**by TA Alice Liu

- Part 3

- Part 1
- Fall 2022 marker board notes
- Part 1
- Digital vs. Analog and the Dirac delta
- Fourier transform of the Dirac delta
- Cellular Communications: basestations, 4G and 5G frequency bands, and companies

- Part 2
- Takeaways from Lecture 3 Part 1
- Determining system linearity property
- Homogeneity property for integrator under observation during class and after class
- In-lecture #1 assignment chirp signal parameters and spectrogram time and frequency resolution
- Handout on Time Invariance for an Integrator

- Part 3
- Handout on time-invariance of an ideal delay under observation
- Continuous-time LTI properties for integrator, ideal delay and sinuosidal amplitude modulation
- Continuous-time finite and infinite impulse response systems
- After-lecture discussion on linearity for an ideal delay

- Part 4

- Part 1
- Spring 2022 marker board notes
- Part 1: Continuous-Time Signals
- Part 2: Continuous-Time Systems
- Part 3: Discrete-Time Systems

- Fall 2021 marker board notes
- time-invariance for an ideal delay
- aliasing analyzed in the time and frequency domains
- LTI property after implementation

- Spring 2021 marker board notes
- Part 1: Z and Fourier transforms, signal properties and Dirac delta properties
- Part 2: continuous-time and discrete-time convolution, and ideal delay
- Part 3: sampling and aliasing

- Fall 2020 marker board notes

Last updated 02/07/24. Send comments to bevans@ece.utexas.edu