My son's eyes got big.
"Oh! Are those the same as Fourier transfers?"
"You mean tranforms?"
"Where did you hear about those?!"
"The Transformers movie."
You may remember (as I vaguely do) the part where they haul
My son's eyes got big.
"Oh! Are those the same as Fourier transfers?"
"You mean tranforms?"
"Where did you hear about those?!"
"The Transformers movie."
You may remember (as I vaguely do) the part where they haul in a bunch of bright people to analyze some sort of signal, and Maggie mentions Fourier Transforms.
Thus, I had to explain what Fourier Transforms are to a thirteen year old who is doing basic algebra.
First, we need a signal:
Let's use the example of the triangle wave. Fourier's idea was that you could make a triangle wave (or any other function) by taking sine (and cosine) waves with different wavelengths and amplitudes and add them together.
Looking at the plot above, you can see that the wavelength (i.e., the distance from one wavecrest to the next) is given by λ. The height of the wave is y. Although the horizontal axis is said to be distance, it could just as easily be time. We can imagine standing at a fixed point, watching the height of the wave as it moves past us and calling out, every second or so, the amplitude of the wave. Thus, we could also say that the wavelength could also be the period, or the amount of time that it takes between wavecrests to move past us.
Fourier's idea is officially called a Fourier Series. Although for the series to equal the function or signal exactly, you could technically need an infinite number of wavelengths. However, you can generally see the idea with just a few waves of