Section 1: Course Overview, Signal Math, Intro to Matlab

A ``section'' is typically two weeks in duration, with the first week devoted primarily to theory, and the second primarily to software and applications.

• Reading
  • This course overview

  • Chapter 1 (DFT Intro) of Mathematics of the DFT.

  • If you are not comfortable with the decibel scale, read Appendix B
    (Logarithms and Decibels)

  • Assignment 1 (complex number problems)

• Supplementary Demos, Reading, and Exercises

  Our main task is to approximate any signal x(t) as a sum of sinusoids $s_\omega(t)$, where the term sinusoid refers to cosine (or sine) having any amplitude A and any phase offset $\phi$:
  

  $$s_\omega(t) = A\cos(\omega t + \phi)$$
  
  
  We call $\omega$ the radian frequency (frequency in radians per second), and $\phi$ the phase of the sinusoid.

  The connection to complex numbers is via Euler's Identity, which can be used to show
  

  $$\cos(\theta) = \frac{e^{j\theta} + e^{-j\theta}}{2}$$
  
  

  The supplementary material below pertains to both sinusoids and complex numbers:

  • But what is a Fourier series? From heat flow to circle drawings | DE4

  • Animation of the Ear doing Spectrum Analysis

  • Brilliant demo of aliasing

  • ``The Acoustic Origins of Harmonic Analysis'' by Olivier Darrigol treatment (published in the Archive for History of the Exact Sciences, vol. 61, no. 4, July 2007)

  • ``History of Virtual Musical Instruments and Effects Based on Physical Modeling Principles'' by JOS, DAFx-2017

  • Interactive Tutorial on Sound, Spectra, and Additive Synthesis

  • Discrete Fourier Transform Demo (Truncated Sinc Spectrum)

  • Building up a Spectrum Analyzer in WebGL

  • For an educational Matlab GUI on sinusoids, download sinedrill from the Educational Matlab GUIs collection at Georgia Tech. There are other nice Matlab-based exercises that can use later in the quarter and next quarter.

  • There is another Matlab GUI illustrating Fourier series approximations, i.e., using sums of sinusoids to approximate classic waveforms such as square wave, sawtooth, and triangle. Download fseriesdemo from the Educational Matlab GUIs collection at Georgia Tech.

  • Interactive demos for Basic physics and signal-processing demos by java@falstad.com
    • In particular, here is nice interactive applet for seeing and optionally hearing the spectra of basic waveforms in your web browser

    • Interactive tool for seeing and hearing classic digital filters (mostly the subject of winter quarter, but we start FIR filters this quarter)

• Chapter 2 (Complex Numbers)

• If you need more practice with complex numbers, work some Khan Academy exercises

• For a Matlab GUI providing complex-number drills, download zdrill from the Educational Matlab GUIs collection at Georgia Tech.

• Here also are some prerequisite-level Khan Academy exercises on dealing with polynomials (you can skip ``Synthetic Division'' and stop before ``Partial Fraction Expansions'' since we get to that in 320B next quarter).

• For more advanced math studies, beyond what's needed for this course, but needed for more advanced signal processing: Georgia Tech Online Mathematics Textbooks

• Lecture Videos:

  IMPORTANT NOTICE: The videos are hosted on YouTube and they use annotations for corrections and supplementary information. These annotations are not supported on mobile devices. It is therefore unfortunately important to view these videos in a Web browser on a desktop/laptop computer.

  • Music 320A Overview (first class recording in fall 2014)
    Introductory Demonstrations for 320A and 320B
  • Administrative overview (this document), discussed only in class (no video), so definitely read it if you missed the first class

  • Intro to the Fourier Transform (FT) and the Discrete Fourier Transform (DFT) [30:52]

  • 3Blue1Brown S4 E4: ``But what is a Fourier series? From heat flow to circle drawings'' [24:46]

  • Albert Michelson's Harmonic Analyzer [First three: 3:30+5:00+3:30]

  • Euler's Identity, Complex Sinusoids [9:43]

  • Complex Plane Intro [4:53]

  • Euler's Identity Corollaries [12:38]

  • Review of DFT and Euler Identity Intro presented 10/02/2014

  • Introduction to Piazza, Coursework, and Matlab [20:08]
    • Regarding the Matlab intro, if you do not know the rules of matrix multiplication, read Appendix H (Matrices).

    • Matlab Documentation

    • Read the first two sections of Appendix J (Matlab Examples) in
      Mathematics of the DFT

    • Do Lab Assignment 0 if you are new to Matlab.