Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

Fourier transforms have a major limitation: They only supply information about the frequencies present in a signal, saying nothing about their timing or quantity. It’s as if you had a process for determining what kinds of bills are in a pile of cash, but not how many of each there actually were. “Wavelets definitely solved this problem, and this is why they are so interesting” A signal could thus be cut up into smaller areas, each centered around a specific wavelength and analyzed by being paired with the matching wavelet. Now faced with a pile of cash, to return to the earlier example, we’d know how many of each kind of bill it contained. Part of what makes wavelets so useful is their versatility, which allow them to decode almost any kind of data. “There are many kinds of wavelets, and you can squish them, stretch them, you can adapt them to the actual image you are looking at”. The wave patterns in digitized images can differ in many aspects, but wavelets can always be stretched or compressed to match sections of the signal with lower or higher frequencies. The shapes of wave patterns can also change drastically, but mathematicians have developed different types, or “families,” of wavelets with different wavelength scales and shapes to match this variability.

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