Week 12 projections, chapter 7

Fourier Transformed my Cat
An objective of learning Fourier Transforms is to be able to laugh at
this joke, and then explain it to your friends. 
IKCD Fourier transformed my cat

Klingon Alphabet
Learning the meaning of the Fourier Transform is at the start similar to
deciphering the Klingon Alphabet.
Klingon Alphabet (JPEG)

Another Klingon Alphabet
Here's a look at the Fourier Transforms of some English letters. The
unintelligible back and white patterns are not the entire transform, but
the image of the magnitude versus frequency (omega). The phase is not
shown. It's another Klingon alphabet.
Letters and their Fourier Transforms (GIF)

Stereo Equalizer and Fourier Series
Sliders on a stereo equalizer adjust the frequency of the signal (a
Fourier series). This is a hands-on way to visualize how Fourier series
and transforms supply frequency information. When you move a slider, it
tunes the magnitude of the corresponding term of matching frequency, in
the signal's Fourier series or transform. Example: Move slider 1200 HZ. 
Then the Fourier series term sin(1200*2*Pi*t) has a re-tuned amplitude. 
Remember: 2Pi/omega=Period, 1/Period=Frequency, HZ=cycles per second.
Stereo equalizer sliders and Fourier transform (PNG)
Approximate frequency ranges for music and voice (GIF)

Importance of Magnitude and Phase
Magnitude and phase are provided by a Fourier Transform. Both are 
required to reconstruct and image.
Slide: Photo, magnitude, phase
Maple: magnitude, phase