EE 313 Linear Systems and Signals - Lecture 3

Before Lecture

• "Roll the Bones", Shakey Graves, 2011.
• Tremolo. The Smiths, "How Soon is Now?", opening guitar riff has a tremolo effect by guitarist Johnny Marr, with a second voice playing slide guitar. Tremolo is rapid change in volume to give a sensation of motion, and is rapidly varying modulation effect. "Songs that Changed Music: The Smiths - How Soon Is Now".
• History of Electronic Music", StomperYoshi, 2013.

Announcements

• Homework #2 is due by 11:59pm on Friday, Sept. 12, 2025, by submission on Gradescope.

Lecture

• Lecture slides on Fourier Series in PowerPoint format.
  • Sum of 440 660 740 Hz part 1 and part 2
  • Harmonic frequencies
  • Simplifying the square of a cosine signal
  • Simplifying exp(-j pi k)

Supplemental Material

• Fall 2023
  • Fall 2023 Part 1
    • Board. Tremolo effect as heard on the song by The Smiths
    • Doc Cam. Beat frequencies of 10 and 1000 Hz
    • Board. Cosine squared has two non-negative frequencies: 0 Hz and twice the cosine frequency
    • Doc Cam. Derivation of Fourier series of cosine squared
    • Board. Beat frequencies of f0-f1 and f0+f1 arise when cos(2 pi f0 t) is multiplied by cos(2 pi f1 t)
  • Fall 2023 Part 2
    • Board. Fourier analysis connecting time and frequency
    • Doc Cam. Fourier series as projection, algorithm to estimate frequency of a cosine, and derivation of Fourier series of cosine squared
    • Doc Cam. Derivation of Fourier series of cosine cubed
  • Derivation of the Fourier series
• Fall 2021: Modulation Property, Sinusoid in time and frequency, Fourier Series
• Fall 2017 audio recording of the presentation on Sept. 14, 2017, of slides 3-7 to 4-4 in MP3 format.

Last updated 09/04/25. Send comments to Prof. Evans at bevans@ece.utexas.edu