Our household WiFi is called FFT. Wala lang. I set it up, and I wanted to use a name that sticks but is not really common. That was two years ago, when I first encountered the Fourier Transform, and also the Fast Fourier Transform. Now, what was then a mathematical tool is now being realized as a very flexible means in image analysis.
This activity is a foray into the properties of the 2D FT. First, we were asked to get the FTs of basic 2D patterns.
Next we observed the anamorphic properties of the Fourier Transform.
Figure 1. FT of sinusoids
In the figure above it is shown that the higher frequency, the more distant the dots of the FTs became. While when the patterns were rotated, below left with theta being 30 degrees and below right with theta being 30 degrees with the addition of another sinusoid. The change in theta caused a shift of the FT, in these cases to the left.
Figure 2. Rotated patterns
On the other hand, when two sinusoids are mulitplied their FT is an addition of their separate FT.
Figure 4. multiplication of multiple sinusoids
Figure 5. Addition of sinusoids
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Some help:
http://how-to.wikia.com/wiki/How_to_plot_in_Scilab
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