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= cos(θ) i sin(θ), you can compress this into one equation: , .There are some important details behind this next bit, but if you expand the size of the interval from [0, 2π] to (-∞, ∞) you get: and Here, instead of C, you have and instead of a summation you have an integral, but the essential idea is the same.An image is another kind of signal, but unlike sound an image is a “two dimensional” signal.A different kind of FT can be still found, and it is likewise two dimensional.
In both math and physics you find that FT’s are floating around behind the scenes in freaking .
If you could see sound, it would look like air molecules bouncing back and forth very quickly.
But oddly enough, when you sound you’re not perceiving the air moving back and forth, instead you experience sound in terms of its frequencies.
Fourier transforms (FT) take a signal and express it in terms of the frequencies of the waves that make up that signal.
Sound is probably the easiest thing to think about when talking about Fourier transforms.