Now that we've been through the whole sequence on Fourier analysis, we can start to understand how we extract that kind of information from a map that looks completely random to the eye. The key is that by applying a variation of Fourier analysis to the map in the picture, we can look for correlations between the fluctuations in the noise. As I explained it, Fourier analysis was able to extract how much of an apparently noisy and random signal was contained in different frequencies - for example, it could pull the individual notes out of the idealized A chord.

An artificially noisy A-chord.

The Fourier transform of the A-chord, with constituent frequencies easily visible.

In that example, the Fourier analysis effectively looks for correlations in time. Because the signal was made up of discrete frequencies, different parts of the signal were related to each other. For example, the A note has a root frequency of 440 Hz, or 440 cycles per second. What that means, although it can be hard to see by eye, is that two parts of the signal separated by 1/440 seconds are related in the way they appear, and the Fourier transform picks up on that. The premise of the CMB analysis is that two areas on the CMB map are also related in the way they appear (just not by eye). Instead of looking for time correlations, they look for spatial correlations in the map using a similar algorithm to the Fourier transform described above. In the next post, I'll show how they decompose the map shown above into its underlying angular or spatial frequencies.

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