EE 313 Linear Systems and Signals - Lecture 2

Before Lecture

• History of Electronic Music", StomperYoshi, 2013.

Announcements

• Homework #1 is due by 11:59pm on Friday, Sept. 6, 2024, by electronic submission via Gradescope.
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  There's also a virtual seminar on Tuesday, Sept. 3, 5-6pm, on how to prepare for the Technology & Science Career Fair.
• Job sites. It's also helpful to post your resume at the Engineering Career Assistance Center, have a LinkedIn page and enable the OpenToWork flag, and search for jobs on LinkedIn.com, Indeed.com, GlassDoor.com, etc.
• Graduate Studies. I have put together suggestions for prospective and current graduate students that I hope are helpful to you.
• Additional Resources.
  • "10 Tips To Help You Network Like a Pro", Editorial Team, Indeed, May 17, 2021
  • "Career Coaches on the Biggest Mistakes People Make in the Job Search", Fast Company, December 9, 2019
  • "50 Best Jobs in America 2023", GlassDoor, based on salary reports and satisfaction surveys.

Lecture

• Lecture slides on Periodic Signals in PowerPoint format.
  • Fall 2024, Part 1
    • Review. The Sampling Theorem says choose the sampling rate f_s so that f_s > 2 f_max where so that frequencies up to and including the frequency of interest, f_max, are captured.
    • Review. Interpreting the Sampling Theorem. We can divide both sides of the inequality f_s > 2 f_max to obtain f_max < (1/2) f_s. That is, sampling at a sampling rate of f_s captures frequencies up to, but not including, (1/2) f_s.
    • Slide 1-20. Zero frequency means a constant signal. Consider x(t) = cos(2 pi f₀ t). Let f₀ = 0, v(t) = cos(2 pi (0 Hz) t) = 1, which is a constant. A constant value (DC value) has a frequency of 0 Hz.
    • Slide 1-20. The playback of the sinusoid at 440 Hz was much quieter than the sinusoid of 440 Hz squared which has a DC component and a component at 880 Hz. Part of the explanation is that the human auditory system has a much stronger response to 880 Hz than 440 Hz. See the A-weighted human hearing curves.
    • Slide 2-4. Phase shift. A phase shift of pi/4 looks the same as a phase shift of 2 pi + pi/4.
    • Slide 2-6. The sampling rate f_s is 1 / T_s.
  • Fall 2024, Part 2
    • Slide 2-8. Inverse Euler's formulas. Convert sinusoidal signals in expressions to complex sinusoids to aid in simplifying the expression.
      • e^{j theta} + e^{-j theta} = 2 cos(theta)
      • e^{j theta} - e^{-j theta} = 2 j sin(theta)
    • Slide 2-9. Even and odd symmetry
    • Slide 2-10. x(t) = cos(2 pi 440 t) which takes values on [-1, 1]. For x(t),
      A₀ = 0
      A₁ = 1, f₁ = 440, phi₁ = 0
      Input x(t) into a squaring block to produce output
      y(t) = x²(t) = cos²(2 pi 440 t) which takes values on [0, 1]. y(t) = (1/2) + (1/2) cos(2 pi (880) t) by using the trigonometric identity for cos²(theta) = (1/2) + (1/2) cos(2 theta). For y(t),
      A₀ = 1/2
      A₁ = 0, f₁ = 440, phi₁ = 0
      A₂ = 1/2, f₂ = 880, phi₂ = 0

Supplemental Material

• Fall 2023
  • Board. Fall 2023 Part 1 Review of continuous vs. discrete time and analog vs. digital amplitude
  • Board. Fall 2023 Part 2: dB scale, exponential response in RC circuit, Euler's formula and summing sinusoids to create a more complicated signal
• Fall 2021: Periodicity review and Fourier analysis of cosine and cosine squared
• Audio recording of the presentation on Sept. 5, 2017, of slides 1-13 to 2-4 in MP3 format
• Audio recording of the presentation on Sept. 7, 2017, of slides 2-5 to 2-12 (last slide) in MP3 format