Supplementary Demos, Reading, and Exercises
Our main task is to approximate any signal x(t) as a sum of
sinusoids , where the term sinusoid refers to
cosine (or sine) having any amplitude A and any phase offset :
We call the radian frequency (frequency in radians per
second), and the phase of the sinusoid.
The connection to complex numbers is via Euler's Identity, which can be used to show
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.
- Tutorial: Visual Complex
Exponentials and Applications in Fourier
Transform
- Interactive demos for
Basic physics and signal-processing demos
by java@falstad.com