Fourier Transform

Fourier transform says that any pattern in space and time can be considered a superposition of sinusoidal patterns with different frequencies. This formula is important because the component frequencies can be used to analyze the patterns, create them to order, extract important features, and remove random noise. Fourier transform led us to image processing and quantum mechanics. It also helped us structure large biological molecules like DNA, do image compression in digital photography, cleaning up old or damaged audio recordings, analyzing earthquakes.